Symbolic dynamics and Markov partitions
| Autor: | Roy L. Adler |
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| Rok vydání: | 1998 |
| Předmět: | |
| Zdroj: | Bulletin of the American Mathematical Society. 35:1-56 |
| ISSN: | 1088-9485 0273-0979 |
| DOI: | 10.1090/s0273-0979-98-00737-x |
| Popis: | The decimal expansion of real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history through a partition. But in order to get a useful symbolism, one needs to construct a partition with special properties. In this work we develop a general theory of representing dynamical systems by symbolic systems by means of so-called Markov partitions. We apply the results to one of the more tractable examples: namely, hyperbolic automorphisms of the two dimensional torus. While there are some results in higher dimensions, this area remains a fertile one for research. |
| Databáze: | OpenAIRE |
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