Shrinking random β-transformation

K. Dajani; K. Jiang

doi:10.1016/j.indag.2016.11.013

Shrinking random β-transformation

K. Dajani
, K. Jiang

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	74-83
Number of pages	10
Journal	Indagationes Mathematicae
Volume	28
Issue number	1
DOIs	https://doi.org/10.1016/j.indag.2016.11.013
Publication status	Published - Feb 2017

Keywords

Random β -transformation;
Unique measure of maximal entropy
Invariant measure

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abstract = "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.",

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AB - 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.

KW - Random β -transformation;

KW - Unique measure of maximal entropy

KW - Invariant measure

U2 - 10.1016/j.indag.2016.11.013

DO - 10.1016/j.indag.2016.11.013

M3 - Article

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SP - 74

EP - 83

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 1

ER -

Shrinking random β-transformation

Abstract

Keywords

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