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Russian Mathematical Surveys, 2006, Volume 61, Issue 1, Pages 1–18
DOI: https://doi.org/10.1070/RM2006v061n01ABEH004297
(Mi rm1714)
 

This article is cited in 20 scientific papers (total in 21 papers)

Forgotten and neglected theories of Poincaré

V. I. Arnol'd

Steklov Mathematical Institute, Russian Academy of Sciences
Abstract: This paper describes a number of published and unpublished works of Henri Poincaré that await continuation by the next generations of mathematicians: works on celestial mechanics, on topology, on the theory of chaos and dynamical systems, and on homology, intersections and links. Also discussed are the history of the theory of relativity and the theory of generalized functions (distributions) and the connection between the Poincaré conjecture and the theory of knot invariants.
Received: 18.08.2005
Bibliographic databases:
Document Type: Article
UDC: 517.91/.93+517.95+515.1+512.7+53
MSC: Primary 01A70; Secondary 57M40, 70F07, 55-03
Language: English
Original paper language: Russian
Citation: V. I. Arnol'd, “Forgotten and neglected theories of Poincaré”, Russian Math. Surveys, 61:1 (2006), 1–18
Citation in format AMSBIB
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\by V.~I.~Arnol'd
\paper Forgotten and neglected theories of Poincar\'e
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 1
\pages 1--18
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Linking options:
  • https://www.mathnet.ru/eng/rm1714
  • https://doi.org/10.1070/RM2006v061n01ABEH004297
  • https://www.mathnet.ru/eng/rm/v61/i1/p3
  • This publication is cited in the following 21 articles:
    1. S. V. Gonchenko, A. S. Gonchenko, K. E. Morozov, “The Third Type of Dynamics and Poincaré Homoclinic Trajectories”, Radiophys Quantum El, 66:9 (2024), 693  crossref
    2. Jaume Llibre, “On the C1 non-integrability of the autonomous differential systems”, Nonlinear Analysis: Real World Applications, 74 (2023), 103943  crossref
    3. R. R. Mukhin, “O teoreme Puankare — Birkgofa kak vazhneishem rezultate teorii dinamicheskikh sistem”, Chebyshevskii sb., 23:1 (2022), 209–222  mathnet  crossref
    4. Alexander G. Aleksandrov, “The Poincaré Index and Its Applications”, Universe, 8:4 (2022), 223  crossref
    5. Moatimid G.M., Elsabaa F.M.F., Zekry M.H., “Approximate Solutions of Coupled Nonlinear Oscillations: Stability Analysis”, J. Appl. Comput. Mech., 7:2 (2021), 382–395  crossref  mathscinet  isi
    6. Ji L. Wang Ch., “Poincare'S Stated Motivations For Topology”, Arch. Hist. Exact Sci., 74:4 (2020), 381–400  crossref  mathscinet  isi
    7. Sololov V., “Discussion of “Multivariate Generalized Hyperbolic Laws For Modeling Financial Log-Returns-Empirical and Theoretical Considerations””, Appl. Stoch. Models. Bus. Ind., 36:5 (2020), 777–779  crossref  mathscinet  isi  scopus
    8. Rutkas A., Vlasenko L., “On a Differential Game in a Nondamped Distributed System”, Math. Meth. Appl. Sci., 42:18 (2019), 6155–6164  crossref  mathscinet  isi  scopus
    9. L. A. Klimina, B. Ya. Lokshin, “Ob odnom konstruktivnom metode poiska rotatsionnykh i avtokolebatelnykh rezhimov v avtonomnykh dinamicheskikh sistemakh”, Nelineinaya dinam., 13:1 (2017), 25–40  mathnet  crossref  elib
    10. Dante Carrasco, Claudio Vidal, “Periodic Solutions, Stability and Non-Integrability in a Generalized Hénon-Heiles Hamiltonian System”, Journal of Nonlinear Mathematical Physics, 20:2 (2013), 199  crossref  mathscinet  isi  scopus
    11. Llibre J., Vidal C., “Periodic orbits and non-integrability in a cosmological scalar field”, J. Math. Phys., 53:1 (2012), 012702, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Jaume Llibre, Clàudia Valls, “A note on the first integrals of the ABC system”, J. Math. Phys, 53:2 (2012), 023505  crossref  mathscinet  zmath  isi  scopus
    13. Lidia Jiménez-Lara, Jaume Llibre, “The cored and logarithm galactic potentials: Periodic orbits and integrability”, J. Math. Phys, 53:4 (2012), 042901  crossref  mathscinet  zmath  adsnasa  isi  scopus
    14. Jiménez-Lara L., Llibre J., “Periodic orbits and nonintegrability of generalized classical Yang–Mills Hamiltonian systems”, J. Math. Phys., 52:3 (2011), 032901, 9 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. Llibre J., Valls C., “On the C1 non-integrability of differential systems via periodic orbits”, European J. Appl. Math., 22:4 (2011), 381–391  crossref  mathscinet  zmath  isi  elib  scopus
    16. Llibre J., Jiménez-Lara l., “Periodic orbits and non-integrability of Hénon–Heiles systems”, J. Phys. A, 44:20 (2011), 205103, 14 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. Llibre J., Valls C., “On the non-integrability of the Belousov–Zhabotinskii system”, Comput. Math. Appl., 62:5 (2011), 2342–2348  crossref  mathscinet  zmath  isi  elib  scopus
    18. Lacomba E.A., Llibre J., “Periodic orbits and non integrability of autonomous Glyden-like systems”, Mathematics and Astronomy: a Joint Long Journey, AIP Conference Proceedings, 1283, 2010, 25–31  crossref  isi  scopus
    19. Navarro-Rosinés P., Calatayud V., Hafellner J., “Contributions to a revision of the genus Cercidospora (Dothideales) 1. Species on Megasporaceae”, Mycotaxon, 110 (2009), 5–25  crossref  isi  scopus
    20. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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