Persistence of the Non-twist Degenerate Lower Dimensional Invariant Torus in Reversible Systems

In this paper, we consider nearly integrable reversible systems, whose unperturbed part has a degenerate equilibrium point and a degenerate frequency mapping. Based on the topological degree theory and some KAM techniques, we prove that the non-twist lower dimensional invariant torus with prescribed...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 23; no. 5
Main Authors Yang, Xiaomei, Xu, Junxiang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.11.2024
Springer Nature B.V
Subjects
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Invariants
Mathematics
Mathematics and Statistics
Toruses
37J25
37J05
Invariant tori
Reversible system
Degenerate equilibrium point
37J40
KAM iteration
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Summary:In this paper, we consider nearly integrable reversible systems, whose unperturbed part has a degenerate equilibrium point and a degenerate frequency mapping. Based on the topological degree theory and some KAM techniques, we prove that the non-twist lower dimensional invariant torus with prescribed frequencies persists under small perturbations.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01108-7