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  • Ergodic Theory and Dynamical Systems, Volume 2, Issue 2
  • June 1982, pp. 195-202

On the subsystems of topological Markov chains

  • Wolfgang Krieger (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385700001516
  • Published online: 01 September 2008
Abstract
Abstract

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.

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[2]M. Denker , Ch. Grillenberger & K. Sigmund . Ergodic Theory on Compact Spaces. Lecture Notes in Math. No. 527. Springer: Berlin, 1976.

[3]H. Kobayashi . A survey of coding schemes for transmission and recording of digital data. IEEE Trans. Comm. 19 (1971), 10871100.

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