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Topological entropy of Markov set-valued functions

Published online by Cambridge University Press:  24 September 2019

LORI ALVIN
Affiliation:
Department of Mathematics, Furman University, Greenville, SC29613, USA email [email protected]
JAMES P. KELLY
Affiliation:
Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA email [email protected]

Abstract

We investigate the entropy for a class of upper semi-continuous set-valued functions, called Markov set-valued functions, that are a generalization of single-valued Markov interval functions. It is known that the entropy of a Markov interval function can be found by calculating the entropy of an associated shift of finite type. In this paper, we construct a similar shift of finite type for Markov set-valued functions and use this shift space to find upper and lower bounds on the entropy of the set-valued function.

Type
Original Article
Copyright
© Cambridge University Press, 2019

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