Introduces integrability notions for C0/C1 natural Hamiltonian systems and gives Liouville-Arnold theorem prototypes, motivated by bungee-jumping models.
A C1 Arnol'd-Liouville theorem
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abstract
In this paper, we prove a version of Arnol'd-Liouville theorem for C 1 commuting Hamiltonians. We show that the Lipschitz regularity of the foliation by invariant Lagrangian tori is crucial to determine the Dynamics on each Lagrangian torus and that the C 1 regularity of the foliation by invariant Lagrangian tori is crucial to prove the continuity of Arnol'd-Liouville coordinates. We also explore various notions of C 0 and Lipschitz integrability.
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math.DS 1years
2026 1verdicts
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From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability
Introduces integrability notions for C0/C1 natural Hamiltonian systems and gives Liouville-Arnold theorem prototypes, motivated by bungee-jumping models.