Author:
DAMRON MICHAEL,FICKENSCHER JON
Abstract
AbstractIf
$\mathcal {A}$
is a finite set (alphabet), the shift dynamical system consists of the space
$\mathcal {A}^{\mathbb {N}}$
of sequences with entries in
$\mathcal {A}$
, along with the left shift operator S. Closed S-invariant subsets are called subshifts and arise naturally as encodings of other systems. In this paper, we study the number of ergodic measures for transitive subshifts under a condition (‘regular bispecial condition’) on the possible extensions of words in the associated language. Our main result shows that under this condition, the subshift can support at most
$({K+1})/{2}$
ergodic measures, where K is the limiting value of
$p(n+1)-p(n)$
, and p is the complexity function of the language. As a consequence, we answer a question of Boshernitzan from 1984, providing a combinatorial proof for the bound on the number of ergodic measures for interval exchange transformations.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
8 articles.
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