Instability for a priori unstable Hamiltonian systems: a dynamical approach
type: Item
instance of: scholarly article
title: Instability for a priori unstable Hamiltonian systems: a dynamical approach
zbMATH Open document ID: 1252.37051
author: Abed Bounemoura
author: Edouard Pennamen
published in: Discrete and Continuous Dynamical Systems
publication date: 2012-03-19T00:00:00Z
review text: The paper considers an a priori unstable 3DOF integrable Hamiltonian system of the form \[ \hat h = \tfrac12(I_1^2+I_2^2) + I_3 + \cos(2\pi\theta_1). \] For a specific perturbation \(H = \hat h + \mu f\), and for \(\mu\) small enough, it is shown that this system has a drifting solution with optimal time of instability. In particular, \(\lim_{t \to \pm \infty} I_2(t) = \pm \infty\) and \(|I_2(\tau) - I_2(0)| \geq 1\) for \(\tau \leq C \mu^{-1} \ln \mu^{-1}\). The proof is based on the construction of symbolic dynamics corresponding to the random iteration of a family of twist maps of the annulus.
reviewed by: Konstantinos Efstathiou
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37D05
Mathematics Subject Classification ID: 37B15
zbMATH DE Number: 6015436
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: perturbation theory
zbMATH Keywords: a priori unstable integrable systems
zbMATH Keywords: Arnold diffusion
MaRDI profile type: Publication
full work available at URL: dcds.2012.32.753
OpenAlex ID: W2316506686
DOI: 10.3934/DCDS.2012.32.753
description: scientific article; zbMATH DE number 6015436