Bifurcation of Closed Orbits of Hamiltonian Systems with Application to Geodesics of the Schwarzschild Metric
Year: 2025
Type: article
Abstract: . We investigate bifurcation of closed orbits with a fixed energy level for a class of nearly integrable Hamiltonian systems with two degrees of freedom. More precisely, we make a joint use of Moser invariant curve theorem and Poincaré–Birkhoff fixed point theorem to prove that a periodic nondegenerate invariant torus [Formula: see text] of the unperturbed problem gives rise to infinitely many closed orbits, bifurcating from a family of tori accumulating onto [Formula: see text]. The required nondegeneracy condition is expressed in terms of the derivative of the apsidal angle with respect to the angular momentum: in this way, tools from the theory of time-maps of nonlinear oscillators can be used to verify it in concrete problems. Applications are given to perturbations of central force problems in the plane, and to equatorial geodesic dynamics for perturbations of the Schwarzschild metric.
DOI: 10.1137/24m1711200
Institutions: University of Turin, University of Udine
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414336163