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Maximal absolutely continuous invariant measures for piecewise linear Markov transformations

Published online by Cambridge University Press:  19 September 2008

W. Byers ,
P. Góra  and
A. Boyarsky
W. Byers
Affiliation:
Department of Mathematics, Concordia University, 7141 Sherbrooke Street West, Montreal H4B 1R6, Canada
P. Góra
Affiliation:
Department of Mathematics, Warsaw University, Warszawa, Poland
A. Boyarsky
Affiliation:
Department of Mathematics, Concordia University, 7141 Sherbrooke Street West, Montreal H4B 1R6, Canada
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Abstract

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Let be an irreducible 0–1 matrix such that the non-zero entries in each row are consecutive. Let be the class of piecewise linear Markov transformations τ on [0, 1] into [0, 1] induced by for which the absolutely continuous invariant measure has maximal entropy. The main result presents necessary and sufficient slope conditions on τ which guarantee that τ ∈ .

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 4 , December 1990 , pp. 645 - 656
Copyright
Copyright © Cambridge University Press 1990

References

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