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On the total variation, topological entropy and sensitivity for interval maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Juang, Jonq Shieh, Shih-Feng Chen, Goong |
| Copyright Year | 2008 |
| 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 . © 2007 Elsevier Inc. All rights reserved. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ir.nctu.edu.tw/bitstream/11536/9331/1/000254588300025.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
