Computing aspects of the entropic theory of one-dimensional dynamical systems
| Autor: | I L Zheleznyak, M I Malkin, A L Zheleznyak |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Polynomial
Dynamical systems theory Applied Mathematics MathematicsofComputing_NUMERICALANALYSIS Measure-preserving dynamical system General Physics and Astronomy Statistical and Nonlinear Physics Topological entropy Lyapunov exponent Topology Topological entropy in physics symbols.namesake symbols Statistical physics Realization (systems) Mathematical Physics Topological quantum number Mathematics |
| Zdroj: | Nonlinearity. 4:27-35 |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/0951-7715/4/1/003 |
| Popis: | The method for computing the topological entropy of the dynamical systems generated by one-dimensional piecewise-continuous piecewise-monotonous maps of interval is proposed. The method is based on the kneading theory and allows one to reduce the computational process to that of seeking the minimum positive zero of some polynomial. A mathematical model of a clock has been studied, which confirmed the high efficiency of the method. The topological entropy is related to the Lyapunov characteristic exponent and to the structure of attractors. The problems involved in the numerical realization of the proposed algorithm are discussed. |
| Databáze: | OpenAIRE |
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