Invariant measures on stationary Bratteli diagrams

被引：42

作者：

Bezuglyi, S. ^{[1
]}

Kwiatkowski, J. ^{[2
]}

Medynets, K. ^{[1
]}

Solomyak, B. ^{[3
]}

机构：

[1] Inst Low Temp Phys, UA-61103 Kharkov, Ukraine

[2] Coll Econ & Comp Sci, PL-10106 Olsztyn, Poland

[3] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2010年 / 30卷

关键词：

SUBSTITUTION DYNAMICAL-SYSTEMS; ORBIT EQUIVALENCE; TRANSFORMATIONS; ERGODICITY; THEOREM; MATRIX; MODELS;

D O I：

10.1017/S0143385709000443

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we give an explicit description of all ergodic probability measures that are invariant with respect to the tail equivalence relation (or the Vershik map); these measures are completely described by the incidence matrix of the Bratteli diagram. Since such diagrams correspond to substitution dynamical systems, our description provides an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.

引用

页码：973 / 1007

页数：35

共 61 条

[41] ON THE SPECTRA OF ADIC TRANSFORMATIONS OF MARKOV COMPACTA [J].