Topologically crossing heteroclinic connections to invariant tori

Marian Gidea*, Clark Robinson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We consider transition tori of Arnold which have topologically crossing heteroclinic connections. We prove the existence of shadowing orbits to a bi-infinite sequence of tori, and of symbolic dynamics near a finite collection of tori. Topologically crossing intersections of stable and unstable manifolds of tori can be found as non-trivial zeroes of certain Melnikov functions. Our treatment relies on an extension of Easton's method of correctly aligned windows due to Zgliczyński.

Original languageEnglish (US)
Pages (from-to)49-74
Number of pages26
JournalJournal of Differential Equations
Volume193
Issue number1
DOIs
StatePublished - Sep 1 2003

Keywords

  • Symbolic dynamics
  • Topological crossing
  • Transition tori

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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