Stability in a Hamiltonian system
type: Item
instance of: scholarly article
title: Stability in a Hamiltonian system
zbMATH Open document ID: 0624.34049
DOI: 10.1007/BF01142477
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: A Hamiltonian system (1) \(\dot x_ j=-\partial H/\partial y_ j\), \(\dot y_ j=\partial H/\partial x_ j\) \((j=1,2)\) where \[ Hu(1-u\rho_ 1+2Re(x_ 1+iy_ 1)^{q_ 1}(x_ 2+iy_ 2)^{q_ 2}), \] u\(=\alpha \rho_ 1+\rho_ 2\), \(\rho_ j=x^ 2_ j+y^ 2_ j\), \(q_ j\geq 3\) are integers, \(\alpha =-q_ 2/q_ 1\) is considered. Theorem. System (1) possesses the following properties. A) In any neighbourhood of the origin every surface defined by \(H=const\) contains invariant tori of (1), B) The origin is not stable in the sense of Lyapunov.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 4013090
zbMATH Keywords: Hamiltonian system
author: A. D. Bryuno
reviewed by: Yu. N. Bibikov
MaRDI profile type: Publication
cites work: Q5686307
cites work: Q3847154
cites work: INSTABILITY IN A HAMILTONIAN SYSTEM AND THE DISTRIBUTION OF ASTEROIDS
full work available at URL: https://doi.org/10.1007/bf01142477
OpenAlex ID: W2055647325
description: scientific article; zbMATH DE number 4013090