School of Mathematics
Loughborough University

Loughborough
Leicestershire
LE11 3TU
UK

Alexey Bolsinov - Publications

Books
  • Topological methods in the theory of integrable systems, Bolsinov A.V., Fomenko A.T., Oshemkov A.A. eds// Cambridge Scientific Publishers, 2006.
  • Bolsinov A.V., Fomenko A.T. Integrable Hamiltonian systems. Geometry, Topology and Classification// CRC Press, 2004 .
    Russian version:
    Bolsinov A.V., Fomenko A.T. Integrable Hamiltonian systems. Geometry, Topology and Classification. Vol. 1, 2 // Izhevsk, Publishing House "Udmurtskii Universitet", 1999.
  • Bolsinov A.V., Fomenko A.T. Integrable geodesic flows on two-dimensional surfaces// Monographs in Contemporary Mathematics. Plenum Acad. Publ., New York, 2000.
    Russian version:
    Bolsinov A.V., Fomenko A.T. The geometry and topology of integrable geodesic flows on surfaces// Moscow, Editorial URSS, 1999, 328 p.

  • Topological methods in the theory of Hamiltonian systems (Collection of papers). Bolsinov A.V., Fomenko A.T., Shafarevich A.I. eds // Moscow, Faktorial, 1998 (in Russian).

  • Bolsinov A.V., Fomenko A.T. Introduction to the topology of integrable systems // Moscow, Nauka, 1997 (in Russian).

  • Papers available in PDF format

  • Bolsinov A. V., Some remarks about Mishchenko-Fomenko subalgebras // arXiv:1405.1710
  • Bolsinov A. V., Singularities of bi-Hamiltonian systems and stability analysis // Lecture Notes of the minicourse given at Centre de Recerca Matematica, Barcelona in September 2013.
  • Bolsinov A. V.; Kazakov A. O.; Kilin A. A., Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra? // arXiv:1401.3630 (accepted by Journal of Geometry and Physics)
  • Bolsinov A. V.; Matveev V. S.; Mettler T.; Rosemann S., Four-dimensional K\"ahler metrics admitting c-projective vector fields // arXiv:1311.0517v1 (accepted by Journal de Math\'ematiques Pures et Appliqu\'ees)
  • Bolsinov A. V.; Tsonev D., On a new class of holonomy groups in pseudo-Riemannian geometry // arXiv:1107.2361 (accepted by J. Diff. Geom.)
  • Bolsinov A. V.; Izosimov A. M., Singularities of bi-Hamiltonian systems // arXiv:1203.3419 (accepted by Comm. Math. Phys.)
  • Bolsinov A. V.; Matveev V. S., Local normal forms for geodesically equivalent pseudo-Riemannian metrics // arXiv:1301.2492v2 (accepted by Trans. Amer. Math. Soc.)
  • A. V. Bolsinov, A. V. Borisov, and I. S. Mamaev, Geometrisation of Chaplygin's reducing multiplier theorem // arXiv:1405.5843 (submitted to Nonlinearity).
  • A. V. Bolsinov, A. V. Borisov, and I. S. Mamaev, Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds // Regul. Chaotic Dyn. 17 (2012), no. 6, 571--579.
  • A. V. Bolsinov, A. V. Borisov, and I. S. Mamaev, Bifurcation analysis and the Conley index in mechanics // Regul. Chaotic Dyn. 17 (2012), no. 5, 451--478.
  • Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S., Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals // Regul. Chaotic Dyn. 17 (2012), no. 6, 571--579.
  • Bolsinov, A. V.; Konyaev, A. Yu., Algebraic and geometric properties of quadratic Hamiltonians defined by sectional operators // Math. Notes 90 (2011), no. 5--6, 666--677.
  • A. V. Bolsinov, A. V. Borisov, and I. S. Mamaev, Topology and stability of integrable systems // Russian Math. Surveys 65(2010), 259--318.
  • Alexey V. Bolsinov, Andrey A. Oshemkov, Bi-Hamiltonian structures and singularities of integrable Hamiltonian systems // Regular and Chaotic Dynamics, 14(2009), 431--454.
  • Alexey V. Bolsinov, Vladimir S. Matveev, Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics // arXiv:0904.0535v1 [math.DG]
  • Alexey V. Bolsinov, Volodymyr Kiosak, Vladimir V. Matveev, A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics // Journal of the London Mathematical Society, 80(2009), 341-356.
  • Alexey V.Bolsinov, Complete commutative subalgebras in polynomial Poisson algebras: a proof of the Mischenko--Fomenko conjecture // revised and extended version of [26].
  • Alexey V. Bolsinov, Konstantin M. Zuev, A formal Frobenius theorem and argument shift // Mathematical Notes 86 (2009), 10--18.
  • Alexey V. Bolsinov, Vladimir S. Matveev, Giuseppe Pucacco, Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta // Journal of Geometry and Physics, 59 (2009), 1048-1062.
  • A. Bolsinov and Yu. Fedorov, Steklov-Lyapunov type systems // Submitted to Journal of Nonlinear Math. Phys.
  • Alexey V. Bolsinov, Bozidar Jovanovic, Magnetic Flows on Homogeneous Spaces // Comm. Math. Helv., 83(2008), 679--700.
  • Chris M.Davison, Holger R.Dullin, Alexey V.Bolsinov, Geodesics on the Ellipsoid and Monodromy // Journal of Geometry and Physics, 57 (2007), 2437-2454.
  • A. V. Bolsinov, H. R. Dullin, A. P. Veselov, Spectra of Sol-Manifolds: Arithmetic and Quantum Monodromy // Comm. Math. Phys., 2006, V.264, pp.583- 611.
  • Alexey V. Bolsinov, Bozidar Jovanovic, Magnetic geodesic flow on coadjoint orbits // J. Phys. A 39 (2006), no. 16, L247- L252.
  • A. Bolsinov, A. Oshemkov, Singularities of integrable Hamiltonian systems // In: Topological Methods in the Theory of Integrable Systems, Cambridge Scientific Publ., 2006, pp. 1-67.
  • Alexey V. Bolsinov, Bozidar Jovanovic Complete involutive algebras of functions on cotangent bundles of homogeneous spaces // Math. Zeit., 2004, Vol. 246, pp. 213-236.
  • Alexey V. Bolsinov, Bozidar Jovanovic, Integrable geodesic flows on Riemannian manifolds: construction and obstructions //In book: Contemporary geometry and related topics, 57- 103, World Sci. Publ., River Edge, NJ, 2004.
  • Alexey V. Bolsinov, Bozidar Jovanovic, Non-commutative integrability, moment map and geodesic flows // Annals of Global Analysis and Geometry 23 (2003), no. 4, 305-322.
  • Alexey V. Bolsinov, Vladimir S. Matveev , Geometrical interpretation of Benenti systems // Jour. Geometry and Physics, 2003, Vol. 44, pp. 489- 506.
  • Alexey V. Bolsinov, Alexey V. Borisov, Compatible Poisson brackets on Lie algebras // Matem. Notes, 2002, V. 72, n. 1, pp. 10-30.
  • Alexey V. Bolsinov, Iskander A. Taimanov , Integrable geodesic flows with positive topological entropy // Invent. Math., 140(2000), pp. 639-650.
  • Alexey V. Bolsinov, Iskander A. Taimanov, Integrable geodesic flows on the suspensions of toric automorphisms // Proc. Steklov Inst. Math. 2000, no. 4 (231), 42- 58.
  • Bolsinov A.V., Borisov A.V., Mamaev I.S. Lie algebras in vortex dynamics and celestial mechanics - IV // Regular and Chaotic Dynamics, 4(1999) No. 1, pp. 23-50.
  • Bolsinov A.V., Dullin H., Wittek A. Topology of energy surfaces and existence of transversal Poincare sections // J. Phys. A: Math. Gen., 29(1996), pp. 4977-4985.

  • Main publications

  • 1. Bolsinov A.V. A completeness criterion for a family of function in involution constructed by the argument shift method// Sov. Math. Dokl., 38(1989) No.1, pp. 161-165.
  • 2. Bolsinov A.V. Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution// Math. USSR Izvestiya, 38(1992) No. 1, pp. 69-89.
  • 3. Bolsinov A.V. Commutative families of functions related to consistent Poisson brackets// Acta Appl. Math., 24(1991), pp. 253-274.
  • 4. Bolsinov A.V. Methods of calculation of Fomenko-Zieschang topological invariant// In book : Advances in Sov. Math., 1991, Vol.6, AMS, Providence, pp. 147-183.
  • 5. Bolsinov A.V., Fedorov Yu.N. Multidimensional integrable generalizations of Steklov-Lyapunov systems// Bull. of Moscow State Univ., ser. 1, 1992, No. 6, pp. 53-56 (in Russian).
  • 6. Bolsinov A.V., Fomenko A.T. Orbital equivalence of integrable systems with two degrees of freedom. The classification theorem. Part I, II// Russian Acad. Sci. Sb. Math. 81(1995), No. 2, pp. 421- 465 and 82(1995), No. 1, pp. 21-63.
  • 7. Bolsinov A.V., Fomenko A.T. Integrable geodesic flows on the sphere generated by Goryachev-Chaplygin and Kovalevskaya systems in rigid body dynamics// Matem. Notes, 56(1994) No. 2, pp. 139-142 (in Russian) .
  • 8. Bolsinov A.V. A smooth trajectory classification of integrable Hamiltonian systems with two degrees of freedom // Sbornik: Mathematics 186(1995) No. 1, pp. 1-27.
  • 9. Bolsinov A.V., Kozlov V.V., Fomenko A.T. Maupertuis principle and the geodesic flows appearing from integrable cases in rigid body dynamics // Russian Math. Surveys, 50(1995) No. 3, pp. 3-32 (in Russian) .
  • 10. Bolsinov A.V., Fomenko A.T. 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 Appl., 29(1995) No. 3, pp. 149-160.
  • 11. Bolsinov A.V., Dullin H., Wittek A. Topology of energy surfaces and existence of transversal Poincare sections // J. Phys. A: Math. Gen., 29(1996), pp. 4977-4985.
  • 12. Bolsinov A.V., Dullin H. On the Euler case in rigid body dynamics and the Jacobi problem // Regular and Chaotic Dynamics, 2(1997) No. 2, pp. 13-25 (in Russian).
  • 13. Bolsinov A.V. Fomenko's invariants in the theory of integrable Hamiltonian systems// Russian Math. Surveys, 52(1997) No. 5(317), pp. 113-132.
  • 14. Bolsinov A.V. Multidimensional Euler and Clebsch cases and Lie pencils// In book: Tensor and Vector Analysis. Gordon and Breach Science Publ., Amsterdam, 1998, pp. 25-30.
  • 15. Bolsinov A.V., Matveev V.S., Fomenko A.T. Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry// Sbornik: Mathematics, 189(1998) No. 10, pp. 1441-1466.
  • 16. Bolsinov A.V., Borisov A.V., Mamaev I.S. Lie algebras in vortex dynamics and celestial mechanics - - IV // Regular and Chaotic Dynamics, 4(1999) No. 1, pp. 23-50.
  • 17. Bolsinov A. V., Taimanov I. A. Integrable geodesic flows with positive topological entropy, // Invent. Math. , 140(2000), pp. 639-650.
  • 18. Bolsinov A. V., Taimanov I. A. Integrable geodesic flows on suspensions of automorphisms of tori// Proc. of the Steklov Institute of Mathematics, 231(2000), pp. 42-58.
  • 19. Bolsinov A.V., Richter P.H., Fomenko A.T. Loop molecule method and the topology of the Kovalevskaya top// Sbornik: Mathematics, 191(2000) No. 2, pp. 151-188.
  • 20. Bolsinov A. V., Jovanovic B. Integrable geodesic flows on homogeneous spaces// Sbornik: Mathematics 192(2001) No. 7, pp. 951-968.
  • 21. Bolsinov A.V., Borisov A.V. Compatible Poisson brackets on Lie algebras// Matem. Notes, 2002, V. 72, n. 1, pp. 11-34 (in Russian).
  • 22. Bolsinov A.V., Matveev V.S. Geometrical interpretation of Benenti systems // Jour. Geometry and Physics, 2003, Vol. 44, pp. 489-506.
  • 23. Bolsinov A., Jovanovic B. Noncommutative integrability, moment map and geodesic flows// Annals of Glob. Anal. and Geom., 2003, Vol. 23, pp. 305-322.
  • 24. Bolsinov A., Jovanovic B. Complete involutive algebras of functions on cotangent bundles of homogeneous spaces// Math. Zeit., 2004, Vol. 246, pp. 213-236.
  • 25. Bolsinov A., Jovanovic B. Integrable geodesic flows on Riemannian manifolds: Construction and Obstructions// In: Proceedings of the Workshop "Contemporary Geometry and Related Topics", Belgrade, 15-21 May 2002. World Scientific Publ. 2004, pp.57-104.
  • 26. Bolsinov A. Complete commutative families of polynomials in Poisson-Lie algebras: A proof of the Mischenko-Fomenko conjecture // In book: Tensor and Vector Analysis, Vol. 26, Moscow State University, 2005, pp. 87-109. (in Russian) .
  • 27. Bolsinov A., Oshemkov A. Singularities of integrable Hamiltonian systems// In: Topological Methods in the Theory of Integrable Systems, Cambridge Scientific Publ., 2006, pp. 1-67.
  • 28. Bolsinov A., Dullin H., Veselov A. Spectra of SOL-manifolds: arithmetic and quantum monodromy // Comm. Math. Phys., 2006, V.264, pp.583- 611.
  • 29. Bolsinov A., Jovanovic B. Magnetic flows on coadjoint orbits// J. Phys. A: Math. Gen., 2006, Vol. 39, L247- L252.
  • 30. Bolsinov A., Jovanovic B. Magnetic flows on homogeneous spaces// Comm. Math. Helv., 2008, Vol.83, pp.679-700.
  • 31. Chris M.Davison, Holger R.Dullin, Alexey V. Bolsinov, Geodesics on the Ellipsoid and Monodromy // Journal of Geometry and Physics, 57 (2007), 2437-2454.
  • 32. Bolsinov A., Oshemkov A., Bi-Hamiltonian structures and singularities of integrable Hamiltonian systems // Regular and Chaotic Dynamics, 14(2009), 431--454.
  • 33. Bolsinov A., Kiosak V., Matveev V. A Fubini theorem for pseudo-Riemannian geodesically equivalent metrics // Journal of the London Mathematical Society, 80(2009), 341-356.
  • 34. Bolsinov A., Zuev K. A formal Frobenius theorem and argument shift // Mathematical Notes 86 (2009), 10--18.
  • 35. Bolsinov A., Matveev V., Pucacco G. Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta // Journal of Geometry and Physics, 59 (2009), 1048-1062.

  • Submitted papers

  • 36. Bolsinov A., Fedorov Yu. Steklov-Lyapunov type systems// Accepted by Journal of Nonlinear Math. Phys.
  • 37. Alexey V. Bolsinov, Vladimir S. Matveev, Splitting and gluing constructions for geodesically equivalent pseudo-Riemannian metrics // Accepted by Trans. Amer. Math. Soc. arXiv:0904.0535v1 [math.DG]

  • Papers in progress

  • 38. Bolsinov A., Matveev V. Symplectic invariants of Liouville foliations and conjugacy of geodesic flows (in preparation).
  • 39. Bolsinov A., Vu Ngoc San, Symplectic equivalence for integrable systems with common action integrals (in prepration).
  • 40. Bolsinov A., Izosimov A. Smooth invariants for multipinched focus singularities of Lagrangian fibrations (in preparation)

  • Recent talks

  • Singularities of Integrable Hamiltonian Systems and their Symplectic Invariants (Joint work with San Vu Ngoc) Dynamical Integrability, CIRM, 27 November - 1 December 2006 (Marseille, France)
  • Non-commutative integrability and Mischenko-Fomenko conjecture, Geometry of Integrable Systems Hanoi National University of Education, April 12, 2007 (Hanoi, Vietnam)
  • Jordan normal form, generalizations and complete integrability, a talk at Math Reviews Seminar, Loughborough University, March 5, 2008 (Loughborough, UK)
  • Singular Lagrangian fibrations and bi-Hamiltonian systems, a talk at the conference ''30 years of bi-Hamiltonian systems'', Bedlewo, Poland, August 2008.
  • Integrable systems on so(n) and geodesically equivalent metrics, a talk at the conference ''Geometry, Dynamics, Integrable Systems'', Belgrade, September 2-7, 2008.
  • Geodesic flows: chaos and integrability University of Liverpool, October 31, 2008
  • Canonical forms for pseudo-Riemannian projectively equivalent metrics: Jordan block case Loughborough University, May 7, 2008
  • Multidimensional focus singularities: invariants, monodromy, classification Monodromy and geometric phases in classical and quantum mechanics, Lorentz Center, June 15--19, 2009 (Leiden, Netherlands)
  • Geodesically equivalent metrics: Splitting lemma Loughborough University, May 26, 2009
  • Topology and Stability of Integrable Systems EQUADIFF 2011, Loughborough, August 2, 2011
  • New holonomy groups in pseudo-Riemannian geometry and integrable systems on Lie algebras Yorkshire Durham Geometry Day, University of York, October 17, 2012
  • Stability analysis and bi-Hamiltonian systems Workshop on Geometric and Analytic Aspects of Integrable Systems, 15 June, 2012, Milano

  • Papers in Russian (PDF)

  • А. В. Болсинов, А. В. Борисов, И. С. Мамаев, Топология и устойчивость интегрируемых систем // Успехи математических наук, 65 (2010), вып. 2 (392), 71--132.
  • А. В. Болсинов, К. М. Зуев, Формальная теорема Фробениуса и метод сдвига аргумента // Матем. заметки 86 (2009), 3--13.
  • А. В. Болсинов, А. В. Борисов, Согласованные скобки Пуассона на алгебрах Ли // Матем. заметки, 2002, 72:1, 11–34
  • А. В. Болсинов, Б. Йованович, Интегрируемые геодезические потоки на однородных пространствах // Матем. сб., 2001, 192:7, 21–40
  • А. В. Болсинов, П. Х. Рихтер, А. Т. Фоменко Метод круговых молекул и топология волчка Ковалевской // Матем. сб., 2000, 191:2, 3–42
  • А. В. Болсинов, В. С. Матвеев, А. Т. Фоменко Двумерные римановы метрики с интегрируемым геодезическим потоком. Локальная и глобальная геометрия // Матем. сб., 1998, 189:10, 5–32
  • А. В. Болсинов Инварианты Фоменко в теории интегрируемых гамильтоновых систем // УМН, 1997, 52:5(317), 113–132
  • А. В. Болсинов, А. Т. Фоменко Траекторная классификация геодезических потоков двумерных эллипсоидов. Задача Якоби траекторно эквивалентна интегрируемому случаю Эйлера в динамике твердого тела // Функц. анализ и его прил., 1995, 29:3, 1–15
  • А. В. Болсинов, В. В. Козлов, А. Т. Фоменко Принцип Мопертюи и геодезические потоки на сфере, возникающие из интегрируемых случаев динамики твердого тела // УМН, 1995, 50:3(303), 3–32
  • А. В. Болсинов Гладкая траекторная классификация интегрируемых гамильтоновых систем с двумя степенями свободы // Матем. сб., 1995, 186:1, 3–28
  • А. В. Болсинов, А. Т. Фоменко Интегрируемые геодезические потоки на сфере, порожденные системами Горячева–Чаплыгина и Ковалевской в динамике твердого тела // Матем. заметки, 1994, 56:2, 139–142
  • А. В. Болсинов, А. Т. Фоменко Траекторная эквивалентность интегрируемых гамильтоновых систем с двумя степенями свободы. Теорема классификации. II // Матем. сб., 1994, 185:5, 27–78
  • А. В. Болсинов, А. Т. Фоменко Траекторная эквивалентность интегрируемых гамильтоновых систем с двумя степенями свободы. Теорема классификации. I // Матем. сб., 1994, 185:4, 27–80
  • А. В. Болсинов Согласованные скобки Пуассона на алгебрах Ли и полнота семейств функций в инволюции // Изв. АН СССР. Сер. матем., 1991, 55:1, 68–92
  • А. В. Болсинов, С. В. Матвеев, А. Т. Фоменко Топологическая классификация интегрируемых гамильтоновых систем с двумя степенями свободы. Список систем малой сложности // УМН, 1990, 45:2(272), 49–77

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