Integral invariants of the Hamilton equations
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.
scientific article; zbMATH DE number 898941