Periodic orbits and Arnold diffusion
type: Item
instance of: scholarly article
title: Periodic orbits and Arnold diffusion
zbMATH Open document ID: 1031.37054
author: Jacky Cresson
author: Christophe Guillet
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-03-01T00:00:00Z
review text: The authors consider three degrees of freedom initially hyperbolic Hamiltonian systems \(H_{\mu}\) with perturbation parameter \(\mu\ll 1.\) Under certain technical assumptions it is shown that the Arnold diffusion time can be of order \(\frac{1}{\mu}\log (\frac{1}{\mu})\) as conjectured by \textit{P. Lochak} [NATO ASI Ser., Ser. C, Math, Phys. Sci. 533, 168-183 (1999; Zbl 0986.37054)]. A dual chain of hyperbolic periodic orbits surrounding a given transition chain of partially hyperbolic tori is constructed. The authors use Easton's method of windows to give a general formula for the time of drift along such a chain of hyperbolic periodic orbits, from which the main result follows.
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1890748
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: Arnold diffusion
zbMATH Keywords: hyperbolic tori
zbMATH Keywords: perturbation
reviewed by: Hans-Bert Rademacher
MaRDI profile type: Publication
full work available at URL: dcds.2003.9.451
OpenAlex ID: W1985484467
DOI: 10.3934/DCDS.2003.9.451
description: scientific article; zbMATH DE number 1890748