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

Jonq Juang, Shih Feng Shieh

研究成果: 雜誌貢獻文章

1 引文 斯高帕斯(Scopus)


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.

頁(從 - 到)1055-1067
期刊Journal of Mathematical Analysis and Applications
出版狀態已發佈 - 2008 五月 15


ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics