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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 1(367), Pages 3–24 (Mi umn1714)  

This article is cited in 15 scientific papers (total in 16 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Abstract: This paper describes a number of published and unpublished works of Henri Poincaré that await continuation by the next generations of mathematicians: works on celestial mechanics, on topology, on the theory of chaos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.


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English version:
Russian Mathematical Surveys, 2006, 61:1, 1–18

Bibliographic databases:

UDC: 517.91/.93+517.95+515.1+512.7+53
MSC: Primary 01A70; Secondary 57M40, 70F07, 55-03
Received: 18.08.2005

Citation: V. I. Arnol'd, “Forgotten and neglected theories of Poincaré”, Uspekhi Mat. Nauk, 61:1(367) (2006), 3–24; Russian Math. Surveys, 61:1 (2006), 1–18

Citation in format AMSBIB
\by V.~I.~Arnol'd
\paper Forgotten and neglected theories of Poincar\'e
\jour Uspekhi Mat. Nauk
\yr 2006
\vol 61
\issue 1(367)
\pages 3--24
\jour Russian Math. Surveys
\yr 2006
\vol 61
\issue 1
\pages 1--18

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    1. Rutkas A., Vlasenko L., “On a Differential Game in a Nondamped Distributed System”, Math. Meth. Appl. Sci.  crossref  isi
    2. Ji L. Wang Ch., “Poincare'S Stated Motivations For Topology”, Arch. Hist. Exact Sci.  crossref  isi
    3. “Vladimir Igorevich Arnol'd (on his 70th birthday)”, Russian Math. Surveys, 62:5 (2007), 1021–1030  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. “Recent publications”, BSHM Bulletin: Journal of the British Society for the History of Mathematics, 22:1 (2007), 72–76  crossref
    5. 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
    6. 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
    7. 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
    8. Llibre J., Valls C., “On the $C^1$ non-integrability of differential systems via periodic orbits”, European J. Appl. Math., 22:4 (2011), 381–391  crossref  mathscinet  zmath  isi  elib  scopus
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