Covering relations for multidimensional dynamical systems. II
type: Item
instance of: scholarly article
title: Covering relations for multidimensional dynamical systems. II
zbMATH Open document ID: 1096.37031
author: Marian Gidea
author: Piotr Zgliczyński
published in: Journal of Differential Equations
publication date: 2004-08-19T00:00:00Z
review text: This article is based on part I [J. Differ. Equations 202, No.~1, 32--58 (2004; Zbl 1061.37013)] by the same authors. Using a topological approach, the authors prove the existence of chaotic orbits in certain Hamiltonian systems with several degrees of freedom. A topological crossing condition for tori replaces the usual transversality and using covering relations, it is shown that arbitrary itineraries to such tori can be realized. The work is based on ideas by \textit{R. W. Easton} [J. Differ. Equations 29, 241--252 (1978; Zbl 0392.58003) and Classical mechanics and dynamical systems, NSF-CBMS reg. Conf., Tufts Univ. 1979, Lect. Notes Pure Appl. Math. 70, 55--67 (1981; Zbl 0502.70024)].
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37B30
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 2092984
zbMATH Keywords: covering relations
zbMATH Keywords: topological crossing
zbMATH Keywords: chaos
reviewed by: Jens D. M. Rademacher
MaRDI profile type: Publication
full work available at URL: j.jde.2004.03.014
OpenAlex ID: W4213080596
cites work: Q4167627
cites work: A geometric criterion for positive topological entropy
cites work: Splitting potential and the Poincaré-Melnikov method for whiskered tori in Hamiltonian systems
cites work: A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: heuristics and rigorous verification on a model
cites work: Homoclinic phenomena in Hamiltonian systems with several degrees of freedom
cites work: Q3968495
cites work: Topologically crossing heteroclinic connections to invariant tori.
cites work: Covering relations for multidimensional dynamical systems
cites work: Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
cites work: Q4547290
DOI: 10.1016/J.JDE.2004.03.014
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description: scientific article; zbMATH DE number 2092984