Journal Articles

Bolsinov, AV, Konyaev, AY, Matveev, VS (2024) Applications of Nijenhuis Geometry V: Geodesic Equivalence and Finite-Dimensional Reductions of Integrable Quasilinear Systems, Journal of Nonlinear Science, 34(2), ISSN: 0938-8974. DOI: 10.1007/s00332-023-10008-0.

Bolsinov, AV, Konyaev, AY, Matveev, VS (2024) Orthogonal separation of variables for spaces of constant curvature, Forum Mathematicum, 0(0), ISSN: 0933-7741. DOI: 10.1515/forum-2023-0300.

Bolsinov, A, Konyaev, A, Matveev, V (2023) Applications of Nijenhuis geometry III: Frobenius pencils and compatible non-homogeneous Poisson structures, The Journal of Geometric Analysis, 33(6), 193, ISSN: 1050-6926. DOI: 10.1007/s12220-023-01237-6.

Bolsinov, A, Konyaev, AY, Matveev, VS (Accepted for publication) Nijenhuis geometry III: gl-regular Nijenhuis operators, Revista Matemática Iberoamericana, ISSN: 0213-2230. DOI: 10.4171/rmi/1416.

Bolsinov, A, Konyaev, AY, Matveev, VS (2023) Applications of Nijenhuis Geometry IV: multicomponent KdV and Camassa-Holm equations, Dynamics of Partial Differential Equations, 20(1), pp.73-98, ISSN: 1548-159X. DOI: 10.4310/DPDE.2023.v20.n1.a4.

Bolsinov, AV, Buchstaber, VM, Veselov, AP, Grinevich, PG, Dynnikov, IA, Kozlov, VV, Kordyukov, YA, Millionshchikov, DV, Mironov, AE, Novikov, RG, Novikov, SP, Yakovlev, AA (2022) Iskander Asanovich Taimanov (on his 60th birthday), Russian Mathematical Surveys, 77(6), pp.1159-1168, ISSN: 0036-0279. DOI: 10.4213/rm10091e.

Bolsinov, A, Matveev, V, Rosemann, S (2021) Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics, Annales Scientifiques de l'Ecole Normale Superieure, 54(6), pp.1465-1540, ISSN: 0012-9593. DOI: 10.24033/asens.2487.

Bolsinov, AV, Veselov, AP, Ye, Y (2021) Chaos and integrability in SL(2,R)-geometry, Russian Mathematical Surveys, 76(4), pp.3-36, ISSN: 0036-0279. DOI: 10.1070/RM10008.

Bolsinov, A, Konyaev, A, Matveev, V (2021) Nijenhuis geometry, Advances in Mathematics, 394, 108001, ISSN: 0001-8708. DOI: 10.1016/j.aim.2021.108001.

Bolsinov, A, Konyaev, A, Matveev, V (2021) Applications of Nijenhuis geometry II: maximal pencils of multihamiltonian structures of hydrodynamic type, Nonlinearity, 34(8), pp.5136-5162, ISSN: 0951-7715. DOI: 10.1088/1361-6544/abed39.

Bolsinov, A, Izosimov, A, Kozlov, I (2021) Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials, Transformation Groups, 28(2), pp.541-560, ISSN: 1083-4362. DOI: 10.1007/s00031-021-09661-0.

Bolsinov, A and Rosemann, S (2021) Local description of Bochner-flat (pseudo-)Kähler metrics, Communications in Analysis and Geometry, 29(3), pp.525-577, ISSN: 1019-8385. DOI: 10.4310/CAG.2021.v29.n3.a1.

Bolsinov, A, Konyaev, A, Matveev, V (2021) Applications of Nijenhuis geometry: non-degenerate singular points of Poisson-Nijenhuis structures, European Journal of Mathematics, 8(4), pp.1355-1376, ISSN: 2199-675X. DOI: 10.1007/s40879-020-00429-6.

Bolsinov, AV, Matveev, VS, Rosemann, S (Accepted for publication) Local normal forms for c-projectively equivalent metrics and proof of the Yano-Obata conjecture in arbitrary signature. Proof of the projective Lichnerowicz conjecture for Lorentzian metrics, Annales Scientifiques de l'Ecole Normale Superieure, ISSN: 0012-9593.

Bolsinov, A and Izosimov, A (2020) Smooth invariants of focus-focus singularities and obstructions to product decomposition, Journal of Symplectic Geometry, 17(6), pp.1613-1648, ISSN: 1527-5256. DOI: 10.4310/JSG.2019.v17.n6.a2.

Bolsinov, A and Bao, J (2019) A Note about Integrable Systems on Low-dimensional Lie Groups and Lie Algebras, Regular and Chaotic Dynamics, 24(3), pp.266-280, ISSN: 1560-3547. DOI: 10.1134/S156035471903002X.

Bolsinov, A (2018) Open Problems, Questions, and Challenges in Finite-Dimensional Integrable Systems, Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, ISSN: 1364-503X. DOI: 10.1098/rsta.2017.0430.

Bolsinov, A, Guglielmi, L, Kudryavtseva, E (2018) Symplectic invariants for parabolic orbits and cusp singularities of integrable systems, Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, ISSN: 1364-503X. DOI: 10.1098/rsta.2017.0424.

Bolsinov, A (2017) Some remarks about Mishchenko-Fomenko subalgebras, Journal of Algebra, 483, pp.58-70, ISSN: 0021-8693.

Bolsinov, AV and Zhang, P (2016) JORDAN–KRONECKER INVARIANTS OF FINITE-DIMENSIONAL LIE ALGEBRAS, Transformation Groups, 21(1), pp.51-86, ISSN: 1083-4362. DOI: 10.1007/s00031-015-9353-6.

Bolsinov, A, Izosimov, A, Tsonev, D (2016) Finite-dimensional integrable systems: a collection of research problems, Journal of Geometry and Physics, ISSN: 0393-0440. DOI: 10.1016/j.geomphys.2016.11.003.

Bolsinov, A (2016) Complete commutative subalgebras in polynomial poisson algebras: a proof of the Mischenko-Fomenko conjecture, Theoretical and Applied Mechanics, ISSN: 1450-5584. DOI: 10.2298/TAM161111012B.

Bolsinov, AV, Borisov, AV, Mamaev, IS (2015) Geometrisation of Chaplygin's reducing multiplier theorem, Nonlinearity, 28(7), pp.2307-2318, ISSN: 0951-7715. DOI: 10.1088/0951-7715/28/7/2307.

Bolsinov, AV, Matveev, VS, Mettler, T, Rosemann, S (2015) Four-dimensional Kähler metrics admitting c-projective vector fields, Journal des Mathematiques Pures et Appliquees, 103(3), pp.619-657, ISSN: 0021-7824. DOI: 10.1016/j.matpur.2014.07.005.

Bolsinov, AV and Matveev, VS (2015) Local normal forms for geodesically equivalent pseudo-Riemannian metrics, Transactions of the American Mathematical Society, 367(9), pp.6719-6749, ISSN: 0002-9947. DOI: 10.1090/s0002-9947-2014-06416-7.

Bizyaev, IA, Bolsinov, A, Borisov, AV, Mamaev, IS (2015) Topology and bifurcations in nonholonomic mechanics, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 25(10), ISSN: 0218-1274. DOI: 10.1142/S0218127415300281.

Bolsinov, A (2015) Argument shift method and sectional operators: applications to differential geometry, Fundamental and Applied Mathematics, ISSN: 1560-5159.

Bolsinov, AV, Kilin, AA, Kazakov, AO (2014) Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?, Journal of Geometry and Physics, 87(2015), pp.61-75, ISSN: 0393-0440. DOI: 10.1016/j.geomphys.2014.08.003.

Bolsinov, A and Tsonev, D (2014) On a new class of holonomy groups in pseudo-Riemannian geometry, Journal of Differential Geometry, 97(3), pp.377-394, ISSN: 0022-040X. DOI: 10.4310/jdg/1406033974.

Bolsinov, A and Kozlov, I (2014) Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials, n/a.

Bolsinov, A and Izosimov, A (2014) Singularities of bi-Hamiltonian systems, Communications in Mathematical Physics, 331(2), pp.507-543, ISSN: 0010-3616. DOI: 10.1007/s00220-014-2048-3.

Bolsinov, AV, Borisov, AV, Mamaev, IS (2012) Bifurcation analysis and the Conley index in mechanics, Regular and Chaotic Dynamics, 17(5), pp.451-478, ISSN: 1560-3547. DOI: 10.1134/S1560354712050073.

Bolsinov, AV, Borisov, AV, Mamaev, IS (2012) Rolling of a ball without spinning on a plane: The absence of an invariant measure in a system with a complete set of integrals, Regular and Chaotic Dynamics, 17(6), pp.571-579, ISSN: 1560-3547. DOI: 10.1134/S1560354712060081.

Bolsinov, AV and Konyaev, AY (2011) Algebraic and geometric properties of quadratic Hamiltonians determined by sectional operators, Mathematical Notes, 90(5-6), pp.666-677, ISSN: 0001-4346. DOI: 10.1134/S0001434611110058.

Bolsinov, AV, Borisov, AV, Mamaev, IS (2011) Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds, Regular and Chaotic Dynamics, 16(5), pp.443-464, ISSN: 1560-3547. DOI: 10.1134/S1560354711050030.

Bolsinov, AV and Matveev, VS (2011) Splitting and gluing lemmas for geodesically equivalent pseudo-Riemannian metrics, Transactions of the American Mathematical Society, 363(8), pp.4081-4107, ISSN: 0002-9947. DOI: 10.1090/S0002-9947-2011-05187-1.

Bolsinov, AV, Borisov, AV, Mamaev, IS (2010) Topology and stability of integrable systems, Russian Math. Surveys, 65, pp.259-318.

Bolsinov, AV, Kiosak, V, Matveev, VS (2009) A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics, Journal of the London Mathematical Society, 80(2), pp.341-356, DOI: 10.1112/jlms/jdp032.

Bolsinov, AV, Matveev, VS, Pucacco, G (2009) Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta, Journal of Geometry and Physics, 59, pp.1048-1062.

Bolsinov, AV and Oshemkov, AA (2009) Bi-Hamiltonian structures and singularties of integrable Hamiltonian systems, Regular and Chaotic Dynamics, 14, pp.431-454.

Bolsinov, AV and Zuev, KM (2009) A formal Frobenious theorem and argument shift, Mathematical Notes, 86, pp.10-18.

Abramov, AM, Arnol'd, VI, Bolsinov, AV, Varchenko, AN, Galgam, L, Zhilinskii, BI, Il'yashenko, YS, Kozlov, VV, Neishtadt, AI, Piterbarg, VI, Khovanskin, AG, Yashchenko, VV (2009) Nikolai Nikolaevich Nekhoroshev (obituary), RUSSIAN MATHEMATICAL SURVEYS, 64(3), pp.561-566, ISSN: 0036-0279. DOI: 10.1070/RM2009v064n03ABEH004622.

Bolsinov, AV and Jovanovic, B (2008) Magnetic Flows on Homogeneous Spaces, Comm. Math. Helv, 83, pp.679-700.

Davison, CM, Dullin, HR, Bolsinov, AV (2007) Geodesics on the Ellipsoid and Monodromy, Journal of Geometry and Physics, 57, pp.2437-2454.

Bolsinov, A, Dullin, HR, Veselov, AP (2006) Spectra of Sol-manifolds: arithmetic and quantum monodromy, Communications in Mathematical Physics, 264(3), pp.583-611, ISSN: 1432-0916. DOI: 10.1007/s00220-006-1543-6.

Bolsinov, AV and Nosov, AP (2006) Chaotic subsystems of integrable hamiltonian systems, Differential Equations, 42(2), pp.298-299, ISSN: 0012-2661. DOI: 10.1134/S0012266106020182.

Bolsinov, AV and Jovanovic, B (2006) Magnetic geodesic flow on coadjoint orbits, Journal of Physics A, 39(16), pp.L247-L252.

Bolsinov, A and Jovanovic, B (2004) Complete involutive algebras of functions on cotangent bundles of homogeneous spaces, Mathematische Zeitschrift, 246(1-2), pp.213-236, ISSN: 1432-1823. DOI: 10.1007/s00209-003-0596-x.

Bolsinov, AV and Fomenko, AT (2004) Integrable Hamiltonian Systems, Geometry, Topology and Classification, CRC Press.

Bolsinov, AV and Jovanovic, B (2003) Integrable geodesic flows on Riemannian manifolds: Construction and Obstructions, Contemporary Geometry and Related Topics (Eds. Bokan N, Djoric M, Rakic Z, Fomenko A. T, Wess J.), World Scientific, 2004, pp.57-103.

Bolsinov, A and Jovanovic, B (2003) Noncommutative integrability, moment map and geodesic flows, Annals of Global Analysis and Geometry, 23(4), pp.305-322, ISSN: 1572-9060. DOI: 10.1023/A:1023023300665.

Bolsinov, A and Jovanovic, B (2003) Geometrical interpretation of Benenti systems, Journal of Geometry and Physics, 44(4), pp.489-506, ISSN: 0393-0440. DOI: 10.1016/S0393-0440(02)00054-2.

Bolsinov, AV and Borisov, AV (2002) Compatible Poisson brackets on Lie algebras, Mathematical Notes, 72(1-2), pp.10-30, ISSN: 0001-4346. DOI: 10.1023/A:1019856702638.

Bolsinov, A and Borisov, AV (2002) Compatible Poisson brackets on Lie algebras, Matem. Notes, 72(1), pp.11-20.

Bolsinov, A and Jovanovic, B (2001) Integrable geodesic flows on homogeneous spaces, Sbornik:Mathematics, 192(7), pp.951-968, ISSN: 1468-4802. DOI: 10.1070/SM2001v192n07ABEH000577.

Bolsinov, AV, Richter, PH, Fomenko, AT (2000) The method of loop molecules and the topology of the Kovalevskaya top, Sbornik Mathematics, 191(1-2), pp.151-188, ISSN: 1064-5616. DOI: 10.1070/sm2000v191n02abeh000451.

Bolsinov, AV and Taimanov, IA (2000) Integrable geodesic flows with positive topological entropy, Inventiones Mathematicae, 140(3), pp.639-650, ISSN: 0020-9910. DOI: 10.1007/s002220000066.

Bolsinov, AV and Taimanov, IA (1999) Integrable geodesic flows on the suspensions of toric automorphisms, Proceedings of the Steklov Institute of Mathematics, 231, pp.42-58, ISSN: 1531-8605.

Bolsinov, AV and Taimanov, IA (1999) On an example of an integrable geodesic flow with positive topological entropy, Russian Mathematical Surveys, 54(4), pp.833-834, ISSN: 0036-0279. DOI: 10.1070/RM1999v054n04ABEH000184.

Bolsinov, AV and Fomenko, AT (1999) Exact topological classification of hamiltonian flows on smooth two-dimensional surfaces, Journal of Mathematical Sciences, 94(4), pp.1457-1476, ISSN: 1072-3374. DOI: 10.1007/BF02365197.

Bolsinov, AV and Matveev, VS (1999) Singularities of momentum maps of integrable hamiltonian systems with two degrees of freedom, Journal of Mathematical Sciences, 94(4), pp.1477-1500, ISSN: 1072-3374. DOI: 10.1007/BF02365198.

Bolsinov, AV, Borisov, AV, Mamaev, IS (1999) Lie algebras in vortex dynamics and celestial mechanics - IV: 1) Classificaton of the algebra of n vortices on a plane 2) Solvable problems of vortex dynamics 3) Algebraization and reduction in a three-body problem, Regular and Chaotic Dynamics, 4(1), pp.23-50, ISSN: 1560-3547. DOI: 10.1070/rd1999v004n01abeh000097.

Bolsinov, AV, Matveev, VS, Fomenko, AT (1998) Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry, Sbornik Mathematics, 189(9-10), pp.1441-1466, ISSN: 1064-5616. DOI: 10.1070/sm1998v189n10abeh000346.

Bolsinov, AV (1997) Fomenko invariants in the theory of integrable Hamiltonian systems, Russian Mathematical Surveys, 52(5), pp.997-1015, ISSN: 0036-0279. DOI: 10.1070/RM1997v052n05ABEH002101.

Bolsinov, A, Dullin, HR, Wittek, A (1996) Topology of Energy Surfaces and Existence of Transversal Poincare Sections, Journal of Physics A, 29, pp.4977-4985.

Bolsinov, AV and Fomenko, AT (1996) Application of classification theory for integrable hamiltonian systems to geodesic flows on 2-sphere and 2-torus and to the description of the topological structure of momentum mapping near singular points, Journal of Mathematical Sciences, 78(5), pp.542-555, ISSN: 1072-3374. DOI: 10.1007/BF02363855.

Bolsinov, AV and Fomenko, AT (1995) Orbital classification of geodesic flows on two-dimensional ellipsoids. The Jacobi problem is orbitally equivalent to the integrable Euler case in rigid body dynamics, Functional Analysis and Its Applications, 29(3), pp.149-160, ISSN: 0016-2663. DOI: 10.1007/BF01077048.

Bolsinov, AV, Kozlov, VV, Fomenko, AT (1995) The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body, Russian Mathematical Surveys, 50(3), pp.473-501, ISSN: 0036-0279. DOI: 10.1070/rm1995v050n03abeh002100.

Bolsinov, AV and Fomenko, AT (1995) A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces, Russian Mathematical Surveys, 50(1), pp.193-194, ISSN: 0036-0279. DOI: 10.1070/rm1995v050n01abeh001665.

Bolsinov, AV and Fomenko, AT (1995) Orbital invariants of integrable Hamiltonian systems. The case of simple systems. Orbital classification of systems of Euler type in rigid body dynamics, Izvestiya: Mathematics, 59(1), pp.63-100, ISSN: 1064-5632. DOI: 10.1070/im1995v059n01abeh000003.

Bolsinov, AV (1995) A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom, Sbornik: Mathematics, 186(1), pp.1-27, ISSN: 1064-5616. DOI: 10.1070/sm1995v186n01abeh000001.

Bolsinov, AV and Fomenko, AT (1995) ORBITAL EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM. A CLASSIFICATION THEOREM. I, Russian Academy of Sciences. Sbornik Mathematics, 81(2), pp.421-465, ISSN: 1064-5616. DOI: 10.1070/sm1995v081n02abeh003545.

Bolsinov, AV and Fomenko, AT (1995) ORBITAL EQUIVALENCE OF INTEGRABLE HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM. A CLASSIFICATION THEOREM. II, Russian Academy of Sciences. Sbornik Mathematics, 82(1), pp.21-63, ISSN: 1064-5616. DOI: 10.1070/sm1995v082n01abeh003551.

Bolsinov, AV (1994) The classification of Hamiltonian systems on two-dimensional surfaces, Russian Mathematical Surveys, 49(6), pp.199-200, ISSN: 0036-0279. DOI: 10.1070/rm1994v049n06abeh002452.

Bolsinov, AV and Fomenko, AT (1994) Integrable geodesic flows on the sphere, generated by Goryachev-Chaplygin and Kowalewski systems in the dynamics of a rigid body, Mathematical Notes, 56(2), pp.859-861, ISSN: 0001-4346. DOI: 10.1007/BF02110747.

Bolsinov, AV (1994) Smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom. The case of systems with planar atoms, Russian Mathematical Surveys, 49(3), pp.181-182, ISSN: 0036-0279. DOI: 10.1070/rm1994v049n03abeh002260.

Bolsinov, AV and Fedorov, YN (1993) Multi-dimensional integrable generalizations of Steklov-Lyapunov systems, Vestnik Moskovskogo Universiteta. Ser. 1 Matematika Mekhanika, (6), pp.53-56, ISSN: 0579-9368.

Bolsinov, AV and Fomenko, AT (1993) Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body, Russian Mathematical Surveys, 48(5), pp.165-166, ISSN: 0036-0279. DOI: 10.1070/rm1993v048n05abeh001076.

Bolsinov, AV (1992) COMPATIBLE POISSON BRACKETS ON LIE ALGEBRAS AND COMPLETENESS OF FAMILIES OF FUNCTIONS IN INVOLUTION, Mathematics of the USSR-Izvestiya, 38(1), pp.69-90, ISSN: 0025-5726. DOI: 10.1070/im1992v038n01abeh002187.

Bolsinov, AV (1991) Commutative families of functions related to consistent Poisson brackets, Acta Applicandae Mathematicae, 24(3), pp.253-274, ISSN: 0167-8019. DOI: 10.1007/BF00047046.

Bolsinov, AV, Matveev, SV, Fomenko, AT (1990) Topological classification of integrable Hamiltonian systems with two degrees of freedom. List of systems of small complexity, Russian Mathematical Surveys, 45(2), pp.59-94, ISSN: 0036-0279. DOI: 10.1070/rm1990v045n02abeh002344.

Bolsinov, AV (1987) Involutory families of functions on dual spaces of Lie algebras of type $ G\underset{\varphi}{+}V$, Russian Mathematical Surveys, 42(6), pp.227-228, ISSN: 0036-0279. DOI: 10.1070/rm1987v042n06abeh001498.

Bolsinov, A and Izosimov, A (Accepted for publication) Singularities of bi-Hamiltonian systems, Communications in Mathematical Physics, 2014, vol. 331, issue 2, pp. 507-543, DOI: 10.1007/s00220-014-2048-3.

Bolsinov, AV, Matveev, VS, Pucacco, G (Accepted for publication) Appendix: Dini theorem for pseudo-Riemannian metrics.

Conferences

Bolsinov, A (2017) Argument shift method and Manakov operators: applications to differential geometry. In LMS EPSRC DURHAM SYMPOSIUM on Geometric and Algebraic Aspects of Integrability, Durham University, Durham, UK.

Bolsinov, A, Vorontsov, A, Zhang, P, Dowell, D, Kozlov, I, Izosimov, A (2016) Jordan-Kronecker invariants of finite-dimensional Lie algebras. In Integrability, Recursion, Geometry And Mechanics, RISM – Villa Toeplitz – Varese, Italy.

Bolsinov, A (2016) Stability analysis, singularities and topology of integrable systems. In Geometry, Dynamics and Integrable Systems, GDIS 2016, Izhevsk, Russia.

Bolsinov, A (2015) Poisson structures and poisson algebras. In Days of Classical Mechanics, Steklov Mathematical Institute, Moscow, Russia.

Bolsinov, A (2015) Argument shift method and sectional operators: applications to differential geometry. In Finite dimensional integrable systems in geometry and mathematical physics, FDIS 2015Argument shift method and sectional operators: applications to diArgument shift method and sectional operators: applications to di, Banach Center, Bedlewo, Poland.

Bolsinov, A (2015) Stability analysis, singularities and topology of integrable systems [Abstract]. In XVIII International Congress on Mathematical Physics, Santiago de Chile.

Bolsinov, A (2014) Integrable geodesic flows of Riemannian and sub-Riemannian metrics on Lie groups and homogeneous spaces. In Scientific semester “Geometry, Analysis and Dynamics on sub-Riemannian manifolds”, IPH, Paris, France.

Bolsinov, A (2013) Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?. In Beyond Toric Integrability, Centre Interfacultaire Bernoulli, Lausanne, Switzerland.

Bolsinov, A (2013) Holonomy groups and special geometries (mini course). In XXXII Workshop on Geometric Methods in Physics, University of Bialystok, Bialowieza, Poland.

Bolsinov, A (2013) Bi-Hamiltonian systems and Jordan-Kronecker invariants of finite-dimensional Lie algebras. In ``2nd Conference on Finite Dimensional Integrable Systems'' FDIS13, CIRM, Marseille, France.

Bolsinov, A (2013) Singularities of bi-Hamiltonian systems and stability analysis (mini course). In ``Advanced Course on Geometry and Dynamics of Integrable Systems'', Centre de Recerca Mathematica, Barcelona, Spain.

Books

Bolsinov, A, Morales-Ruiz, JJ, Zung, NT (2016) Geometry and dynamics of integrable systems, Birkhäuser © Springer International Publishing, ISBN: 9783319335032. DOI: 10.1007/978-3-319-33503-2.

Bolsinov, AV and Fomenko, AT (2004) Integrable Hamiltonian Systems, CRC Press, ISBN: 9780415298056.

Bolsinov, AV and Fomenko, AT (2004) Integrable hamiltonian systems: Geometry topology classification,ISBN: 9780415298056.

Bolsinov, AV and Fomenko, AT (2000) Integrable geodesic flows on two-dimensional surfaces, Plenum Pub Corp, ISBN: 9780306110658.

Chapters

Bolsinov, A (2018) Integrable geodesic flows. In Trends in Mathematics, © Springer, pp.237-243, ISBN: 9783319635934. DOI: 10.1007/978-3-319-63594-1_23.

Bolsinov, A (2016) Singularities of bi-Hamiltonian systems and stability analysis. In Unknown Parent Title, © Springer, pp.35-84, DOI: 10.1007/978-3-319-33503-2.

Bolsinov, A and Oshemkov, A (2006) Singularities of integrable Hamiltonian systems. In Unknown Parent Title, Topological Methods in the Theory of Integrable Systems, pp.1-67.

Bolsinov, A (2005) Complete commutative families of polynomials in Poisson-Lie algebras: A proof of the Mischenko-Fomenko conjecture. In Unknown Parent Title, Tensor and Vector Analysis, Vol. 26, pp.87-109.

Internet Publications

Bolsinov, A, Konyaev, AY, Matveev, VS (2020) Applications of Nijenhuis geometry II: maximal pencils of multihamiltonian structures of hydrodynamic type.

Other

Bolsinov, A, Matveev, VS, Tabachnikov, S (2022) Editors’ foreword for the special issue “New Developments in Integrable Systems”. DOI: 10.1007/s40879-022-00587-9.

Bolsinov, AV and Rosemann, S (2021) Local description of Bochner-Flat (pseudo-)Kahler metrics, The Bochner tensor is the Kähler analogue of the conformal Weyl tensor. In this article, we derive local (i.e, in a neighbourhood of almost every point) normal forms for a (pseudo-)Kähler manifold with vanishing Bochner tensor. The description is pined down to a new class of symmetric spaces which we describe in terms of their curvature operators. We also give a local description of weakly Bochner-flat metrics defined by the property that the Bochner tensor has vanishing divergence. Our results are based on the local normal forms for c-projectively equivalent metrics. As a byproduct, we also describe all Kähler-Einstein metrics admitting a c-projectively equivalent one. DOI: 10.4310/CAG.2021.v29.n3.a1.

Bolsinov, A and Izosimov, A (2019) Smooth invariants of focus-focus singularities and obstructions to product decomposition, We study focus-focus singularities (also known as nodal singularities, or pinched tori) of Lagrangian fibrations on symplectic 4-manifolds. We show that, in contrast to elliptic and hyperbolic singularities, there exist homeomorphic focus-focus singularities which are not diffeomorphic. Furthermore, we obtain an algebraic description of the moduli space of focus-focus singularities up to smooth equivalence, and show that for double pinched tori this space is one-dimensional. Finally, we apply our construction to disprove Zung’s conjecture which says that any non-degenerate singularity can be smoothly decomposed into an almost direct product of standard singularities. DOI: 10.4310/JSG.2019.v17.n6.a2.

Bolsinov, AV, Konyaev, AY, Matveev, VS (2019) Nijenhuis Geometry, This work is the first, and main, of the series of papers in progress dedicated to Nienhuis operators, i.e, fields of endomorphisms with vanishing Nijenhuis tensor. It serves as an introduction to Nijenhuis Geometry that should be understood in much wider context than before: from local description at generic points to singularities and global analysis. The goal of the present paper is to introduce terminology, develop new important techniques (e.g, analytic functions of Nijenhuis operators, splitting theorem and linearisation), summarise and generalise basic facts (some of which are already known but we give new self-contained proofs), and more importantly, to demonstrate that the research programme proposed in the paper is realistic by proving a series of new, not at all obvious, results..

Bolsinov, A, Guglielmi, L, Kudryavtseva, E (2018) Symplectic invariants for parabolic orbits and cusp singularities of integrable systems, We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We also suggest some new techniques which apparently can be used for studying symplectic invariants of degenerate singularities of more general type. This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.. DOI: 10.1098/rsta.2017.0424.

Bolsinov, A, Matveev, VS, Miranda, E, Tabachnikov, S (2018) Open problems, questions and challenges in finite- dimensional integrable systems, The paper surveys open problems and questions related to different aspects of integrable systems with finitely many degrees of freedom. Many of the open problems were suggested by the participants of the conference ‘Finite-dimensional Integrable Systems, FDIS 2017’ held at CRM, Barcelona in July 2017.This article is part of the theme issue ‘Finite dimensional integrable systems: new trends and methods’.. DOI: 10.1098/rsta.2017.0430.

Bolsinov, A and Tsonev, D (Accepted for publication) On one class of holonomy groups in pseudo-Riemannian geometry, We describe a new class of holonomy groups on pseudo-Riemannian manifolds. Namely, we prove the following theorem. Let g be a nondegenerate bilinear form on a vector space V, and L:V -> V a g-symmetric operator. Then the identity component of the centraliser of L in SO(g) is a holonomy group for a suitable Levi-Civita connection..

Bolsinov, A, Konyaev, AY, Matveev, VS (Accepted for publication) Array, We study and completely describe pairs of compatible Poisson structures near singular points of the recursion operator satisfying natural non-degeneracy condition..

Bolsinov, A, Konyaev, A, Matveev, V (Accepted for publication) Nijnehuis Geometry III: gl-regular Nijenhuis operators, We study Nijenhuis operators, that is, (1,1)-tensors with vanishing Nijenhuis torsion under the additional assumption that they are gl-regular, i.e, every eigenvalue has geometric multiplicity one. We prove the existence of a coordinate system in which the operator takes first or second companion form, and give a local describtion of such operators. We apply this local description to study singular points. In particular, we obtain their normal forms in dimension two and discover topological restrictions for the existence of gl-regular Nijenhuis operators on closed surfaces. This paper is an important step in the research programme suggested in arXiv:1903.04603 and arXiv:1903.06411..