標題: On the total variation, topological entropy and sensitivity for interval maps
作者: Juang, Jonq
Shieh, Shih-Feng
應用數學系
Department of Applied Mathematics
關鍵字: interval maps;total variation;topological entropy;sensitivity
公開日期: 15-五月-2008
摘要: A concept related to total variation termed H-1 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 H-1 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 H-1 condition of a piecewise-monotone continuous map implies the non-restrictiveness of the map. In addition, we also show that either H-1 condition or sensitivity then gives the positivity of the topological entropy of f. (C) 2007 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jmaa.2007.11.013
http://hdl.handle.net/11536/9331
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.11.013
期刊: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume: 341
Issue: 2
起始頁: 1055
結束頁: 1067
顯示於類別:期刊論文


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