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Generalized baker's transformations

Published online by Cambridge University Press:  19 September 2008

Christopher J. Bose
Christopher J. Bose
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, USA
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Abstract

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A class of automorphisms of the unit square called generalized baker'stransformations (gbt) is defined in such a way that every stationary stochastic process may be represented as the movement of a simple partition of the square under a gbt. This extends the classical example of the representation of independent processes by the well-known baker's transformation.

Every ergodic, positive-entropy automorphism is measurably isomorphic to some gbt (again generalizing the classical result about Bernoulli shifts), and we show that a large class of gbt's satisfying certain continuity restrictions are actually measurably isomorphic to Bernoulli shifts.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 1 , March 1989 , pp. 1 - 17
Copyright
Copyright © Cambridge University Press 1989

References

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