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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On endomorphisms of a solenoid


Author: A. M. Wilson
Journal: Proc. Amer. Math. Soc. 55 (1976), 69-74
DOI: https://doi.org/10.1090/S0002-9939-1976-0390181-7
MathSciNet review: 0390181
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Abstract: Geometrically simple Bernoulli generators are constructed for certain ergodic endomorphisms of solenoids. An arbitrary ergodic solenoidal group automorphism is obtained as the limit of a sequence of such Bernoulli factors and hence, by a theorem of D. S. Ornstein, must be measure-theoretically isomorphic to a Bernoulli shift.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0390181-7
Keywords: Solenoid, topological group endomorphism, Bernoulli shift, natural extension, generalised Bernoulli shift
Article copyright: © Copyright 1976 American Mathematical Society