Mathematical Notes

, Volume 58, Issue 3, pp 938–947 | Cite as

Integral invariants of the Hamilton equations

  • V. V. Kozlov


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.


Hamiltonian System Analytic Surface Hamilton Equation Constant Multiple Geodesic Flow 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • V. V. Kozlov
    • 1
  1. 1.Moscow State UniversityUSSR

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