تقرير
Equilibrium States for the Random $\beta$-Transformation through $g$-Measures
| العنوان: | Equilibrium States for the Random $\beta$-Transformation through $g$-Measures |
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| المؤلفون: | Dajani, Karma, Power, Kieran |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, 37E05, 28D05, 37E15, 37A45, 37A05 |
| الوصف: | We consider the random $\beta$-transformation $K_{\beta}$, defined on $\{0,1\}^{\mathbb N}\times[0, \frac{\lfloor\beta\rfloor}{\beta-1}]$, that generates all possible expansions of the form $x=\sum_{i=0}^{\infty}\frac{a_i}{\beta^i}$, where $a_i\in \{0,1,\cdots,\lfloor\beta\rfloor\}$. This transformation was first introduced by Dajani and Kraaikamp, and later studied by Dajani and de Vries, where two natural invariant ergodic measures were found. The first is the unique measure of maximal entropy, and the second is a measure of the form $m_p\times \mu_{\beta}$, with $m_p$ the Bernoulli $(p,1-p)$ product measure and $\mu_{\beta}$ is a measure equivalent to Lebesgue measure. In this paper, we give an uncountable family of $K_{\beta}$-invariant exact $g$-measures for a certain collection of algebraic $\beta$'s. Comment: 15 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2104.11634 |
| رقم الأكسشن: | edsarx.2104.11634 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |