On the total variation, topological entropy and sensitivity for interval maps

Juang Jonq, Shih Feng Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

A concept related to total variation termed H1 condition was recently proposed to characterize the chaotic behavior of an interval map f by Chen, Huang and Huang [G. Chen, T. Huang, Y. Huang, Chaotic behavior of interval maps and total variations of iterates, Internat. J. Bifur. Chaos 14 (2004) 2161-2186]. In this paper, we establish connections between H1 condition, sensitivity and topological entropy for interval maps. First, we introduce a notion of restrictiveness of a piecewise-monotone continuous interval map. We then prove that H1 condition of a piecewise-monotone continuous map implies the non-restrictiveness of the map. In addition, we also show that either H1 condition or sensitivity then gives the positivity of the topological entropy of f.

Original languageEnglish
Pages (from-to)1055-1067
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume341
Issue number2
DOIs
StatePublished - 15 May 2008

Keywords

  • Interval maps
  • Sensitivity
  • Topological entropy
  • Total variation

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