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How does a choice of Markov partition affect the resultant symbolic dynamics?
| Title: | How does a choice of Markov partition affect the resultant symbolic dynamics? |
| Authors: | Teramoto, Hiroshi Browse this author | | Komatsuzaki, Tamiki Browse this author |
| Keywords: | Markov processes | | nonlinear dynamical systems | | time series |
| Issue Date: | Sep-2010 |
| Publisher: | American Institute of Physics |
| Journal Title: | Chaos |
| Volume: | 20 |
| Issue: | 3 |
| Start Page: | 037113 |
| Publisher DOI: | 10.1063/1.3491097 |
| PMID: | 20887079 |
| Abstract: | The mutual relationship among Markov partitions is investigated for one-dimensional piecewise monotonic map. It is shown that if a Markov partition is regarded as a map-refinement of the other Markov partition, that is, a concept we newly introduce in this article, one can uniquely translate a set of symbolic sequences by one Markov partition to those by the other or vice versa. However, the set of symbolic sequences constructed using Markov partitions is not necessarily translated with each other if there exists no map-refinement relation among them. By using a roof map we demonstrate how the resultant symbolic sequences depend on the choice of Markov partitions. |
| Rights: | Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Chaos 20, 037113 (2010) and may be found at https://dx.doi.org/10.1063/1.3491097 |
| Type: | article |
| URI: | http://hdl.handle.net/2115/44123 |
| Appears in Collections: | 電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 寺本 央
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