Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian system
type: Item
instance of: scholarly article
title: Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian system
zbMATH Open document ID: 1483.37080
author: Tianqi Jing
author: Wen Si
published in: Journal of Differential Equations
publication date: 2021-08-16T00:00:00Z
review text: The main result of the paper is about the existence of lower-dimensional tori for a class of degenerate Hamiltonian systems, that are also supposed to be only \(C^\ell\) smooth. This is a generalization of known results for which the degenerate case was considered within the analytic class, or the loss of analyticity was considered in the non-degenerate case. The proof is ruled out in the framework of KAM theory. The loss of regularity is overcome via the Jackson-Moser-Zehnder analytic approximation, while the degeneracy is treated through normal form theory for quasi-homogeneous polynomial systems and the stability of equilibrium points of odd degree polynomials. Some applications of the main theorem are given.
reviewed by: Stefano Marò
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 70H08
Mathematics Subject Classification ID: 70K43
zbMATH DE Number: 7382032
zbMATH Keywords: Moser-type theorem
zbMATH Keywords: smooth Hamiltonian system
zbMATH Keywords: regularity
zbMATH Keywords: degenerate lower-dimensional tori
zbMATH Keywords: KAM theory
MaRDI profile type: Publication
full work available at URL: j.jde.2021.07.028
OpenAlex ID: W3194819634
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DOI: 10.1016/J.JDE.2021.07.028
description: scientific article; zbMATH DE number 7382032