2018年10月
Universality of the route to chaos: Exact analysis
PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS
- ,
- 巻
- 2018
- 号
- 10
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1093/ptep/pty094
- 出版者・発行元
- OXFORD UNIV PRESS INC
The universality of the route to chaos is analytically proven for a countably infinite number of maps by proposing Super Generalized Boole (SGB) transformations. One of the routes to chaos, the intermittency route, was previously studied extensively by numerical methods. These researchers conjectured the universality in Type 1 intermittency, namely that the critical exponent of the Lyapunov exponent in this type of intermittency is 1/2. We prove their conjecture by showing that, for certain parameter ranges, the SGB transformations are exact and preserve the Cauchy distribution. Using the property of exactness, we prove that the critical exponent is 1/2 for a countably infinite number of maps where Type 1 intermittency occurs.
- リンク情報
- ID情報
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- DOI : 10.1093/ptep/pty094
- ISSN : 2050-3911
- Web of Science ID : WOS:000450277800001