Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity
Dynamical Systems
2025-10-08 v1
Abstract
We prove that, on each low energy level, the natural Hamiltonian system defined by a generic smooth potential on exhibits an arbitrarily high number of hyperbolic periodic orbits and a positive-measure set of invariant tori. Hence, quasi-periodic motion and hyperbolic behavior typically coexist in the low-energy dynamics of natural Hamiltonian systems with two degrees of freedom.
Cite
@article{arxiv.2510.06073,
title = {Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity},
author = {Alberto Enciso and Manuel Garzón and Daniel Peralta-Salas},
journal= {arXiv preprint arXiv:2510.06073},
year = {2025}
}