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Entropy and finite generators for locally compact subshifts

Published online by Cambridge University Press:  17 April 2001

DORIS FIEBIG  and
ULF-RAINER FIEBIG
DORIS FIEBIG
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany (e-mail: fiebig@math.uni-heidelberg.de)
ULF-RAINER FIEBIG
Affiliation:
Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany (e-mail: fiebig@math.uni-heidelberg.de)
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Abstract

We introduce transition entropy and periodic entropy for locally compact subshifts. Finiteness of both characterizes the existence of a finite generator. Finiteness of the transition entropy characterizes the existence of a generator with bounded degree. We extend Krieger's embedding theorem and characterize the locally compact non-dense subsystems of a (compact) mixing shift of finite type.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 2 , April 1997 , pp. 349 - 368
Copyright
1997 Cambridge University Press

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