Shrinking random β-transformation
| Autor: | Dajani, K., Jiang, K., Sub Mathematical Modeling, Mathematical Modeling |
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| Rok vydání: | 2017 |
| Předmět: |
General Mathematics
010102 general mathematics 020206 networking & telecommunications 02 engineering and technology 01 natural sciences Invariant measure Unique measure of maximal entropy Combinatorics Maximal entropy Taverne 0202 electrical engineering electronic engineering information engineering Ergodic theory 0101 mathematics Invariant (mathematics) Random β -transformation Mathematics Real number |
| Zdroj: | Indagationes Mathematicae, 28(1), 74. Elsevier |
| ISSN: | 0019-3577 |
| Popis: | For any n ≥ 3 , let 1 β 2 be the largest positive real number satisfying the equation β n = β n − 2 + β n − 3 + ⋯ + β + 1 . In this paper we define the shrinking random β -transformation K and investigate natural invariant measures for K , and the induced transformation of K on a special subset of the domain. We prove that both transformations have a unique measure of maximal entropy. However, the measure induced from the intrinsically ergodic measure for K is not the intrinsically ergodic measure for the induced system. |
| Databáze: | OpenAIRE |
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