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arXiv · 2505.05369

The multi-scale KAM persistence without a scaling order for Hamiltonian systems

Weichao Qian·Yong Li·Xue Yang
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Abstract

The persistence of invariant tori in multi-scale Hamiltonian systems is intrinsically linked to the stability of the N-body problem. However, the existing non-degeneracy conditions in disordered scenarios have been formulated too generally, making them difficult to apply directly to celestial mechanics. In this work, we present a readily verifiable non-degeneracy condition for the persistence of invariant tori in disordered multi-scale Hamiltonian systems.

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Weichao Qian, Yong Li, Xue Yang. 2025-05-08. The multi-scale KAM persistence without a scaling order for Hamiltonian systems. https://arxiv.org/abs/2505.05369

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