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On the subsystems of topological Markov chains

Published online by Cambridge University Press:  19 September 2008

Wolfgang Krieger
Wolfgang Krieger
Affiliation:
Institut für Angewandte Mathematik der Universität Heidelberg, Im Neuenheimer Feld 294, D-6900, Heidelberg 1
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Abstract

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Let SA be an irreducible and aperiodic topological Markov chain. If SĀ is an irreducible and aperiodic topological Markov chain, whose topological entropy is less than that of SA, then there exists an irreducible and aperiodic topological Markov chain, whose topological entropy equals the topological entropy at SĀ, and that is a subsystem of SA. If S is an expansive homeomorphism of the Cantor discontinuum, whose topological entropy is less than that of SA, and such that for every j∈ℕ the number of periodic points of least period j of S is less than or equal to the number of periodic points of least period j of SA, then S is topological conjugate to a subsystem of SA.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 2 , June 1982, pp. 195 - 202
Copyright
Copyright © Cambridge University Press 1982

References

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