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An example of a factor map without a saturated compensation function

Published online by Cambridge University Press:  28 November 2001

SUJIN SHIN
SUJIN SHIN
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada, V8W 3P4 (e-mail: shin@math.uvic.ca)
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Abstract

Let (X, S), (Y, T) be topological dynamical systems and \pi : X \rightarrow Y a factor map. A function F \in C(X) is a compensation function if P (F + \phi \circ \pi) = P (\phi) for all \phi \in C(Y). We present an example of a factor map \pi : X \rightarrow Y between subshifts of finite type X, Y that does not have a saturated compensation function and an example of a non-Markovian factor map with a saturated compensation function. Also we provide a necessary and sufficient condition for a certain type of factor map to have a saturated compensation function.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001 , pp. 1855 - 1866
Copyright
2001 Cambridge University Press

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