Expansivity and shadowing in subspaces

Andy D Barwell, Chris Good, Piotr Oprocha

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)

Abstract

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval.

Original languageEnglish
Pages (from-to)223-243
Number of pages21
JournalFundamenta Mathematicae
Volume219
Issue number3
DOIs
Publication statusPublished - 2013

Keywords

  • OMEGA-LIMIT SETS
  • expanding map
  • interval map
  • DYNAMICAL-SYSTEMS
  • shadowing
  • expansivity
  • APPROXIMATE
  • pseudo-orbit tracing
  • TENT MAPS
  • expansive map

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