Chaos for implicit difference equations with snap-back repellers

Hung Ju Chen, Ming-Chia Li*, Shi Xuan Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is a study of chaos for generalized dynamical systems derived from implicit difference equations. We define a snap-back repeller for an implicit difference equation and show that its existence implies chaotic dynamics for all small C1-perturbed systems. By chaotic dynamics, we mean that the solution set of an implicit difference equation contains a compact subset on which the Bernoulli shift map is invariant and has positive topological entropy.

Original languageEnglish
Pages (from-to)180-191
Number of pages12
JournalJournal of Difference Equations and Applications
Volume24
Issue number2
DOIs
StatePublished - 1 Feb 2018

Keywords

  • chaos
  • Difference equation
  • perturbation
  • topological entropy

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