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Mat. Zametki, 1995, Volume 58, Issue 3, Pages 379–393 (Mi mz2055)  

Integral invariants of the Hamilton equations

V. V. Kozlov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Conditions are found for the existence of integral invariants of Hamiltonian systems. For two-degrees-of-freedom systems these conditions are intimately related to the existence of nontrivial symmetry fields and multivalued integrals. Any integral invariant of a geodesic flow on an analytic surface of genus greater than 1 is shown to be a constant multiple of the Poincaré–Cartan invariant. Poincaré's conjecture that there are no additional integral invariants in the restricted three-body problem is proved.

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English version:
Mathematical Notes, 1995, 58:3, 938–947

Bibliographic databases:

Document Type: Article
Received: 02.12.1994

Citation: V. V. Kozlov, “Integral invariants of the Hamilton equations”, Mat. Zametki, 58:3 (1995), 379–393; Math. Notes, 58:3 (1995), 938–947

Citation in format AMSBIB
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\by V.~V.~Kozlov
\paper Integral invariants of the Hamilton equations
\jour Mat. Zametki
\yr 1995
\vol 58
\issue 3
\pages 379--393
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1368547}
\zmath{https://zbmath.org/?q=an:0853.58052}
\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 3
\pages 938--947
\crossref{https://doi.org/10.1007/BF02304771}
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