2016年8月

# Continuous orbit equivalence of topological Markov shifts and dynamical zeta functions

ERGODIC THEORY AND DYNAMICAL SYSTEMS
• Kengo Matsumoto
• ,
• Hiroki Matui

36
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1557

1581

DOI
10.1017/etds.2014.128

CAMBRIDGE UNIV PRESS

For continuously orbit equivalent one-sided topological Markov shifts. (X-A, sigma(A)) and. (X-B, sigma(B)), their eventually periodic points and cocycle functions are studied. As a result, we directly construct an isomorphism between their ordered cohomology groups ((H) over bar (A), (H) over bar (A)(+)) and ((H) over bar (B), (H) over bar (B)(+)) We also show that the cocycle functions for the continuous orbit equivalences give rise to positive elements of their ordered cohomology groups, so that the zeta functions of continuously orbit equivalent topological Markov shifts are related. The set of Borel measures is shown to be invariant under continuous orbit equivalence of one-sided topological Markov shifts.

Web of Science ® 被引用回数 : 4

リンク情報
DOI
https://doi.org/10.1017/etds.2014.128
Web of Science