Stability of equilibrium points for a Hamiltonian systems with two degrees of freedom in the problem of parametric resonance
type: Item
instance of: scholarly article
title: Stability of equilibrium points for a Hamiltonian systems with two degrees of freedom in the problem of parametric resonance
DOI: 10.1134/S1995080222090037
author: A. S. Belova
published in: Lobachevskii Journal of Mathematics
publication date: 2022-11-15T00:00:00Z
review text: The question about stability of periodic Hamiltonian systems is a classical topic in Hamiltonian dynamics. The present paper is focused on Hamiltonian systems with two degrees of freedom, with emphasis on the case for which the unperturbed linearized equations has resonances. The article is written on a clear-cut basis and provides sufficient conditions for achieving stable or unstable equilibrium points.
reviewed by: J. M. Hoff da Silva
Mathematics Subject Classification ID: 37J25
Mathematics Subject Classification ID: 37J46
Mathematics Subject Classification ID: 37J12
Mathematics Subject Classification ID: 70H14
Mathematics Subject Classification ID: 70K28
Mathematics Subject Classification ID: 70K30
zbMATH DE Number: 7616994
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: equilibrium point
zbMATH Keywords: stability
zbMATH Keywords: multiplier
zbMATH Keywords: small parameter
zbMATH Keywords: parametric resonance
MaRDI profile type: Publication
cites work: Q5151953
cites work: Normalization of a periodic Hamiltonian system
cites work: On the stability of equilibria in two-degrees-of- freedom Hamiltonian systems under resonances
cites work: Q2978235
cites work: Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
cites work: Perturbation theory methods in problem of parametric resonance for linear periodic Hamiltonian systems
cites work: Q5535170
cites work: Q5559761
cites work: Approximate research of problems on perturbation of periodic and autonomous Hamiltonian systems in critical cases
description: scientific article; zbMATH DE number 7616994