Integral invariants of the Hamilton equations
type: Item
instance of: scholarly article
title: Integral invariants of the Hamilton equations
zbMATH Open document ID: 0853.58052
DOI: 10.1007/BF02304771
author: Valery V. Kozlov
published in: Mathematical Notes
publication date: 1997-01-05T00:00:00Z
review text: The author establishes conditions for the existence of integral invariants of Hamiltonian systems. For systems with two degrees of freedom, these conditions are intimately linked to the existence of non-trivial symmetries. The author shows that any integral invariant of a geodesic flow on an analytic surface whose genus is greater than one must be a constant multiple of the Poincaré-Cartan invariant. In addition, the author establishes the non-existence of additional integral invariants for the restricted three-body problem.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 70H33
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 70F07
zbMATH DE Number: 898941
zbMATH Keywords: integral invariants
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Poincaré-Cartan invariant
zbMATH Keywords: restricted three-body problem
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 898941