A Formal KAM Theorem for Hamiltonian Systems and Its Application to Hyperbolic Lower Dimensional Invariant Tori

In this paper we reformulate a formal KAM theorem for Hamiltonian systems with parameters under Bruno-Rüssmann condition. The proof is based on KAM iteration and the key is to adjust the parameters for small divisors after KAM iteration instead of in each KAM step. By this formal KAM theorem we can...

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Bibliographic Details
Published inQualitative theory of dynamical systems Vol. 23; no. 2
Main Authors Li, Qi, Xu, Junxiang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2024
Springer Nature B.V
Subjects
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Hamiltonian functions
Invariants
Mathematics
Mathematics and Statistics
Parameters
Theorems
Toruses
Formal KAM theorem
Bruno-Rüssmann condition
KAM iteration
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Summary:In this paper we reformulate a formal KAM theorem for Hamiltonian systems with parameters under Bruno-Rüssmann condition. The proof is based on KAM iteration and the key is to adjust the parameters for small divisors after KAM iteration instead of in each KAM step. By this formal KAM theorem we can follow some well known KAM-type results for hyperbolic tori. Moreover, it can also be applied to the persistence of invariant tori with prescribed frequencies.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-023-00938-1