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arXiv · 2606.00870

From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability

Vladimir Dragović·Borislav Gajić·Božidar Jovanović
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Abstract

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.

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Vladimir Dragović, Borislav Gajić, Božidar Jovanović. 2026-05-30. From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability. https://arxiv.org/abs/2606.00870

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