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Matematicheskie Zametki, 1995, Volume 58, Issue 3, Pages 379–393 (Mi mzm2055)  
Integral invariants of the Hamilton equations

V. V. Kozlov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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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.
Received: 02.12.1994
English version:
Mathematical Notes, 1995, Volume 58, Issue 3, Pages 938–947
DOI: https://doi.org/10.1007/BF02304771
Bibliographic databases:
Document Type: Article
Language: Russian
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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\jour Math. Notes
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\issue 3
\pages 938--947
\crossref{https://doi.org/10.1007/BF02304771}
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