Frequency extraction from invariant flows.

Authors

Derong Xu, Yongjun Li, Yue Hao, Sergei Nagaitsev

Published in

Physical review. E. Volume 114. Issue 3. Pages L032202.

Abstract

In nondegenerate integrable Hamiltonian systems, invariant tori can be parametrized by action variables or fundamental frequencies. We introduce an invariant-flow formulation, consistent with the Liouville-Arnold geometry, for extracting these frequencies. Treating invariants as generators of commuting Hamiltonian flows yields the frequencies from time-of-flight parameters, providing a direct alternative to action-angle constructions and long-time spectral analysis. The resulting numerical procedure extends naturally to multiple degrees of freedom and achieves high accuracy for the McMillan map. More broadly, the framework provides an invariant-centered view of near-integrable dynamics, recovering frequencies and other dynamical information from high-quality approximate invariants.

PMID:
42888790
Bibliographic data and abstract were imported from PubMed on 17 Oct 2026.

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