Open AccessA KAM theorem for quasi-periodic non-twist mappings and its application
Author(s) -
Zhichao Ma,
JiQing Xu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2022013
Subject(s) - twist , invariant (physics) , intersection (aeronautics) , property (philosophy) , mathematics , kolmogorov–arnold–moser theorem , pure mathematics , order (exchange) , stability (learning theory) , mathematical analysis , computer science , geometry , mathematical physics , integrable system , philosophy , epistemology , machine learning , engineering , aerospace engineering , finance , economics
In this paper we consider quasi-periodic non-twist mappings with self-intersection property, which depend on a small parameter. Without assuming any twist condition, we prove that for many sufficiently small parameters the mapping admits an invariant curve. As application, we use this result to study Lagrange stability of second order systems.