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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.06073 |
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| _version_ | 1866916994826108928 |
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| author | Enciso, Alberto Garzón, Manuel Peralta-Salas, Daniel |
| author_facet | Enciso, Alberto Garzón, Manuel Peralta-Salas, Daniel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity Enciso, Alberto Garzón, Manuel Peralta-Salas, Daniel Dynamical Systems 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. |
| title | Low-energy dynamics in generic potential fields: Hyperbolic periodic orbits and non-ergodicity |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2510.06073 |