Graph duality in surface dynamics

Pieter Collins, Kevin Mitchell

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We compare one-dimensional representations for the isotopy stable dynamics of homeomorphisms in two dimensions. We consider the skeleton graph representative, which captures periodic behaviour, and the homotopy graph representative which captures homo/heteroclinic behaviour. The main result of this paper is to show that the dual to the skeleton graph representative is the homotopy graph representative of the inverse map. This gives a strong link between different methods for computing the dynamics.
Original languageEnglish
Pages (from-to)2103-2135
Number of pages33
JournalJournal of Nonlinear Science
Volume29
Issue number5
DOIs
Publication statusPublished - Oct 2019

Keywords

  • CHAOS
  • DIFFEOMORPHISMS
  • Dual graph
  • Fixed-point theory
  • GEOMETRY
  • Homoclinic
  • Homotopy lobe dynamics
  • Symbolic dynamics
  • TOPOLOGICAL FLUID-MECHANICS
  • TRANSPORT
  • Train tracks
  • heteroclinic tangles

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