Integral invariants of the Hamilton equations (Q1916635)
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scientific article; zbMATH DE number 898941
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Integral invariants of the Hamilton equations |
scientific article; zbMATH DE number 898941 |
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Integral invariants of the Hamilton equations (English)
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5 January 1997
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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.
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integral invariants
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Hamiltonian systems
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Poincaré-Cartan invariant
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restricted three-body problem
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