Symbolic dynamics and Arnold diffusion
type: Item
instance of: scholarly article
title: Symbolic dynamics and Arnold diffusion
zbMATH Open document ID: 1018.37038
DOI: 10.1016/S0022-0396(02)00053-0
author: Jacky Cresson
published in: Journal of Differential Equations
publication date: 2003-03-18T00:00:00Z
review text: The author considers Graff tori of three degrees of freedom initially hyperbolic Hamiltonian systems [\textit{S. M. Graff}, J. Differ. Equations 15, 1-69 (1974; Zbl 0257.34048)] and extends the classical Birkhoff-Smale theorem for hyperbolic points or normally hyperbolic tori to partially hyperbolic Graff tori. The main result: if the stable and unstable manifold of a partially hyperbolic Graff tori intersect transversally, then there exists a hyperbolic invariant set near a homoclinic orbit on which the dynamics is conjugated to a Bernoulli shift. The existence of infinitely many hyperbolic periodic orbits near the given torus is deduced. Then the relevance of these results for the instability of near-integrable Hamiltonian systems is discussed.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37B10
zbMATH DE Number: 1884222
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: hyperbolic tori
zbMATH Keywords: symbolic dynamic
zbMATH Keywords: Birkhoff-Smale theorem
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1884222