Perturbations of geodesic flows and lengths of the closed geodesics
Perturbations of geodesic flows and lengths of the closed geodesics
The author considers the ``geometric perturbation'' of the Hamiltonian of a geodesic flow on a surface of constant negative curvature. This corresponds to a deformation of the metric which according to Guillemin and Kazhdan's theorem must be induced by local coordinate transformations. On the other hand by a result of Collet, Epstein, and Gallavotti perturbed and unperturbed Hamiltonians are canonically conjugate. The aim of this paper is to prove that, in this case, the canonical conjugation is ``geometric'', i.e. it is induced on the cotangent bundle by a coordinate transformation on the surface.
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, geodesic flow, negative curvature, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, perturbations of Hamiltonians, geometric perturbation, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, geodesic flow, negative curvature, Canonical and symplectic transformations for problems in Hamiltonian and Lagrangian mechanics, perturbations of Hamiltonians, geometric perturbation, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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