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Funktsional. Anal. i Prilozhen., 1997, Volume 31, Issue 1, Pages 3–11 (Mi faa441)  

This article is cited in 19 scientific papers (total in 19 papers)

The Absence of an Additional Real-Analytic First Integral in Some Problems of Dynamic

S. L. Ziglin

Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

DOI: https://doi.org/10.4213/faa441

Full text: PDF file (966 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 1997, 31:1, 3–9

Bibliographic databases:

UDC: 517.913
Received: 19.05.1995
Revised: 27.08.1996

Citation: S. L. Ziglin, “The Absence of an Additional Real-Analytic First Integral in Some Problems of Dynamic”, Funktsional. Anal. i Prilozhen., 31:1 (1997), 3–11; Funct. Anal. Appl., 31:1 (1997), 3–9

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. L. Ziglin, “Integrals in Involution for Groups of Linear Symplectic Transformations and Natural Mechanical Systems with Homogeneous Potential”, Funct. Anal. Appl., 34:3 (2000), 179–187  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Maciejewski, AJ, “Towards a description of complexity of the simplest cosmological systems”, Journal of Physics A-Mathematical and General, 33:50 (2000), 9241  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Maciejewski A.J., “Non-integrability in gravitational and cosmological models - Introduction to Ziglin theory and its differential Galois extension”, Restless Universe - Applications of Gravitational N-Body Dynamics To Planetary, Stellar and Galactic Systems, Scottish Universities Summer Schools in Physics Publications, 54, 2001, 361–385  crossref  isi
    4. Audin, M, “Integrability and non-integrability of Hamiltonian systems (after S. Ziglin, J. Morales-Ruiz, J.-P. Ramis)”, Asterisque, 2002, no. 282, 113  mathscinet  zmath  isi
    5. Maciejewski, A, “Non-integrability of ABC flow”, Physics Letters A, 303:4 (2002), 265  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Maciejewski, AJ, “Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields”, Celestial Mechanics & Dynamical Astronomy, 87:4 (2003), 317  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Maciejewski, AJ, “Nonintegrability of the Suslov problem”, Journal of Mathematical Physics, 45:3 (2004), 1065  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Maciejewski, AJ, “Non-integrability of Gross-Neveu systems”, Physica D-Nonlinear Phenomena, 201:3–4 (2005), 249  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Audin M., “Two notions of integrability”, Differential Equations and Quantum Groups - ANDREY A. BOLIBRUKH MEMORIAL VOLUME, Irma Lectures in Mathematics and Theoretical Physics, 9, 2007, 27–47  mathscinet  zmath  isi
    10. Fedorov Y.N., Maciejewski A.J., Przybylska M., “The Poisson Equations in the Nonholonomic Suslov Problem: Integrability, Meromorphic and Hypergeometric Solutions”, Geometric Methods in Physics, AIP Conference Proceedings, 1191, 2009, 85–90  crossref  mathscinet  adsnasa  isi  scopus
    11. Morales-Ruiz J.J., Ramis J.-P., “Integrability of Dynamical Systems through Differential Galois theory: a practical guide”, Differential Algebra, Complex Analysis and Orthogonal Polynomials, Contemporary Mathematics, 509, 2010, 143–220  crossref  mathscinet  zmath  isi
    12. Mahdi A., Valls C., “Analytic Non-Integrability of the Suslov Problem”, J. Math. Phys., 53:12 (2012), 122901  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Maciejewski A.J., Przybylska M., “Integrable Variational Equations of Non-Integrable Systems”, Regul. Chaotic Dyn., 17:3-4 (2012), 337–358  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. van der Heijden G.H.M. Yagasaki K., “Horseshoes For the Nearly Symmetric Heavy TOP”, Z. Angew. Math. Phys., 65:2 (2014), 221–240  crossref  mathscinet  zmath  isi  scopus
    15. Yehia H.M., Elmandouh A.A., “A new conditional integrable case in the dynamics of a rigid body-gyrostat”, Mech. Res. Commun., 78:A (2016), 25–27  crossref  mathscinet  isi  scopus
    16. Popov S. Strelcyn J.-M., “The Euler-Poisson Equations: An Elementary Approach to Integrability Conditions”, J. Geom. Mech., 10:3 (2018), 293–329  crossref  isi  scopus
    17. Ershkov S.V., Leshchenko D., “On a New Type of Solving Procedure For Euler-Poisson Equations (Rigid Body Rotation Over the Fixed Point)”, Acta Mech., 230:3 (2019), 871–883  crossref  mathscinet  isi  scopus
    18. Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520  mathscinet  isi
    19. Kazuyuki Yagasaki, Shogo Yamanaka, “Heteroclinic Orbits and Nonintegrability in Two-Degree-of-Freedom Hamiltonian Systems with Saddle-Centers”, SIGMA, 15 (2019), 049, 17 pp.  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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