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arXiv · 2510.06073

Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity

Alberto Enciso·Manuel Garzón·Daniel Peralta-Salas
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Abstract

We prove that, on each low energy level, the natural Hamiltonian system defined by a generic smooth potential on $\mathbf{T}^2$ 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.

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Alberto Enciso, Manuel Garzón, Daniel Peralta-Salas. 2025-10-07. Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity. https://arxiv.org/abs/2510.06073

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