1997年5月
Method of constructing exactly solvable chaos
PHYSICAL REVIEW E
- 巻
- 55
- 号
- 5
- 開始ページ
- 5280
- 終了ページ
- 5284
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevE.55.5280
- 出版者・発行元
- AMERICAN PHYSICAL SOC
We present a systematic method of constructing rational mappings as er odic transformations with nonuniform invariant measures on the unit interval I = [0,1]. As a result, we obtain a two-parameter family of rational mappings that have a special property in that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is shown here that this family is the most generalized class of rational mappings possessing the property of exactly solvable chaos on I, including the Ulam-von Neumann map y = 4x(1-x). Based on the present method, we can produce a series of rational mappings resembling the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction, and we can match some rational functions with other experimentally obtained first return maps in a systematic manner.
- リンク情報
- ID情報
-
- DOI : 10.1103/PhysRevE.55.5280
- ISSN : 1063-651X
- Web of Science ID : WOS:A1997XB19100054