From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability
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| Natura: | Preprint |
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2026
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| _version_ | 1866910276625891328 |
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| author | Dragović, Vladimir Gajić, Borislav Jovanović, Božidar |
| author_facet | Dragović, Vladimir Gajić, Borislav Jovanović, Božidar |
| contents | We consider natural Hamiltonian systems with potentials that are $C^0$ or $C^1$ on a hypersurface and $C^{\infty}$-smooth in the complement and introduce and study corresponding notions of their integrabilty and non-integrability. As a motivating example, we derive and analyze models of bungee jumping. We provide prototype examples of the Liuoville-Arnol'd theorem for $C^0$ and $C^1$ Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00870 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability Dragović, Vladimir Gajić, Borislav Jovanović, Božidar Dynamical Systems Mathematical Physics Exactly Solvable and Integrable Systems 37J35, 37E40, 70H06, 70H07, 37C83, 34A38 We consider natural Hamiltonian systems with potentials that are $C^0$ or $C^1$ on a hypersurface and $C^{\infty}$-smooth in the complement and introduce and study corresponding notions of their integrabilty and non-integrability. As a motivating example, we derive and analyze models of bungee jumping. We provide prototype examples of the Liuoville-Arnol'd theorem for $C^0$ and $C^1$ Hamiltonians. |
| title | From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability |
| topic | Dynamical Systems Mathematical Physics Exactly Solvable and Integrable Systems 37J35, 37E40, 70H06, 70H07, 37C83, 34A38 |
| url | https://arxiv.org/abs/2606.00870 |