Invariant sets of degenerate Hamiltonian systems near equilibria
type: Item
instance of: scholarly article
title: Invariant sets of degenerate Hamiltonian systems near equilibria
zbMATH Open document ID: 0940.70012
published in: Regular and Chaotic Dynamics
publication date: 2000-07-17T00:00:00Z
review text: It is proved that, for any collection of \(n\) frequencies \(\omega_i\), there exists a \(C^\infty\) Hamiltonian system with \(n\) degrees of freedom which has an elliptic equilibrium at 0, \(\omega_i\) are the corresponding eigenfrequencies, the Hamiltonian vector field is linear up to a remainder which is flat at 0, and the measure of the set of the \(n\)-dimensional invariant tori in a \(\varepsilon\)--neighborhood of 0 tends to zero with \(\varepsilon\), faster than any prescribed function. The same result is valid for symplectic maps and also for reversible flows and maps.
reviewed by: Simos Ichtiaroglou
Mathematics Subject Classification ID: 70H05
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 1340946
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: symplectic maps
zbMATH Keywords: invariant tori
zbMATH Keywords: elliptic equilibrium
zbMATH Keywords: eigenfrequencies
author: Mikhail Sevryuk
MaRDI profile type: Publication
DOI: 10.1070/RD1998V003N03ABEH000082
description: scientific article; zbMATH DE number 1340946