Chain transitivity in hyperspaces

Leobardo Fernández*, Christopher Good, Mate Puljiz, Ártico Ramírez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
14 Downloads (Pure)

Abstract

Given a non-empty compact metric space X and a continuous function f: X → X, we study the dynamics of the induced maps on the hyperspace of non-empty compact subsets of X and on various other invariant subspaces thereof, in particular symmetric products. We show how some important dynamical properties transfer across induced systems. These amongst others include, chain transitivity, chain (weakly) mixing, chain recurrence, exactness by chains. From our main theorem we derive an ε-chain version of Furstenberg's celebrated 2 implies n Theorem. We also show the implications our results have for dynamics on continua.

Original languageEnglish
Pages (from-to)83-90
Number of pages8
JournalChaos, Solitons and Fractals
Volume81
Issue numberPart A
Early online date21 Sept 2015
DOIs
Publication statusPublished - 1 Dec 2015

Keywords

  • Chain transitivity
  • Chain weakly mixing
  • Exact by chains
  • Induced map
  • δ-pseudo orbit

ASJC Scopus subject areas

  • General Mathematics

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