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Ergodic endomorphisms of compact abelian groups

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Abstract

We show that for a surjective endomorphism of a compact abelian group ergodicity is equivalent to a condition which impliesr-mixing for allr≧1, and we characterize such maps algebraically. This is then used in proving the ergodicity of an extensive class of endomorphisms of the binary sequence space. As a simple corollary it is found that one-dimensional linear cellular automata and the accumulator automata arer-mixing for allr≧1.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada

    M. Shirvani & T. D. Rogers

Authors
  1. M. Shirvani
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  2. T. D. Rogers
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Additional information

Communicated by J.-P. Eckmann

This work was supported in part by grants from NSERC

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Shirvani, M., Rogers, T.D. Ergodic endomorphisms of compact abelian groups. Commun.Math. Phys. 118, 401–410 (1988). https://doi.org/10.1007/BF01466724

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  • DOI: https://doi.org/10.1007/BF01466724

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