Integral invariants of the Hamilton equations. (English. Russian original) Zbl 0853.58052
Math. Notes 58, No. 3, 938-947 (1995); translation from Mat. Zametki 58, No. 3, 379-393 (1995).
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.
Reviewer: W.J.Satzer jun.(St.Paul)
MSC:
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
| 70H33 | Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics |
| 37D40 | Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) |
| 53D25 | Geodesic flows in symplectic geometry and contact geometry |
| 70F07 | Three-body problems |
Keywords:
integral invariants; Hamiltonian systems; Poincaré-Cartan invariant; restricted three-body problemReferences:
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