Open AccessOn the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations
Author(s) -
Xiaocai Wang,
Xiaofei Cao,
Xuqing Liu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022004
Subject(s) - torus , degenerate energy levels , ergodic theory , persistence (discontinuity) , mathematics , generalization , invariant (physics) , pure mathematics , statistical physics , mathematical analysis , physics , mathematical physics , geometry , quantum mechanics , geotechnical engineering , engineering
This paper focuses on the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations. By an improved KAM iteration and Topological degree theory, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [On the persistence of degenerate lower-dimensional tori in reversible systems, Ergodic Theory Dynam. Systems, 35(2015), 2311-2333].