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Integral invariants of the Hamilton equations

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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.

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Authors and Affiliations

  1. Moscow State University, USSR

    V. V. Kozlov

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  1. V. V. Kozlov
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Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 379–393, September, 1995.

The work was financially supported by the Russian Foundation for Basic Research (grant No. 242 93-013-16244), International Science Foundation (grant No. MCY 000), and INTAS (grant No. 93-339).

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Kozlov, V.V. Integral invariants of the Hamilton equations. Math Notes 58, 938–947 (1995). https://doi.org/10.1007/BF02304771

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