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Topological entropy of Markov set-valued functions

Part of:Maps and general types of spaces defined by mapsTopological dynamics

Published online by Cambridge University Press:  24 September 2019

LORI ALVIN and
JAMES P. KELLY
LORI ALVIN
Affiliation:
Department of Mathematics, Furman University, Greenville, SC 29613, USA email lori.alvin@furman.edu
JAMES P. KELLY
Affiliation:
Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA email james.kelly@cnu.edu
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Abstract

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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.

Keywords

entropyMarkov partitionsymbolic dynamicsset-valued function

MSC classification

Primary:37B40: Topological entropy37B10: Symbolic dynamics54C60: Set-valued maps

Information

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 2 , February 2021, pp. 321 - 337
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Copyright
© Cambridge University Press, 2019

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