Shrinking random -transformation

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• 作者：Kan Jiang ; Karma Dajani ; ^{k.dajani1@uu.nl}
• 关键词：Random ββ-transformation ; Unique measure of maximal entropy ; Invariant measure
• 刊名：Indagationes Mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：28
• 期：1
• 页码：74-83
• 全文大小：227 K
• 卷排序：28

文摘

For any n≥3n≥3, let 1<β<21<β<2 be the largest positive real number satisfying the equation βn=βn−2+βn−3+⋯+β+1.βn=βn−2+βn−3+⋯+β+1. In this paper we define the shrinking random ββ-transformation KK and investigate natural invariant measures for KK, and the induced transformation of KK 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 KK is not the intrinsically ergodic measure for the induced system.