Shadowing, asymptotic shadowing and s-limit shadowing

Chris Good, Piotr Oprocha, Mate Puljiz

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
214 Downloads (Pure)

Abstract

We study three notions of shadowing: classical shadowing, limit (or asymptotic) shadowing, and s-limit shadowing. We show that classical and s-limit shadowing coincide for tent maps and, more generally, for piecewise linear interval maps with constant slopes, and are further equivalent to the linking property introduced by Chen in 1991. We also construct a system which exhibits shadowing but not limit shadowing, and we study how shadowing properties transfer to maximal transitive subsystems and inverse limits (sometimes called natural extensions). Where practicable, we show that our results are best possible by means of examples.

Original languageEnglish
Pages (from-to)287-312
Number of pages26
JournalFundamenta Mathematicae
Volume244
Issue number3
Early online date21 Dec 2018
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Internally chain transitive sets,
  • Interval maps,
  • Linking property,
  • Shadowing property,
  • Symbolic dynamics
  • ω-limit sets,

ASJC Scopus subject areas

  • Algebra and Number Theory

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