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On the existence of ergodic continuous invariant measures for folding transformations

Published online by Cambridge University Press:  01 February 2000

ABRAHAM BOYARSKY,
PAWEL GÓRA and
VADIM LIOUBIMOV
ABRAHAM BOYARSKY
Affiliation:
Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada (e-mail: boyar@vax2.concordia.ca, pgora@vax2.concordia.ca, vadim@alcor.concordia.ca)
PAWEL GÓRA
Affiliation:
Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada (e-mail: boyar@vax2.concordia.ca, pgora@vax2.concordia.ca, vadim@alcor.concordia.ca)
VADIM LIOUBIMOV
Affiliation:
Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke Street West, Montreal, Quebec H4B 1R6, Canada (e-mail: boyar@vax2.concordia.ca, pgora@vax2.concordia.ca, vadim@alcor.concordia.ca)
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Abstract

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We present a sufficient condition for the existence of ergodic continuous invariant measures (ECIMs) for continuous folding transformations. We apply this result to prove the existence of ECIMs for general set expanding Markov transformations and $n$-dimensional tent maps.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 1 , February 2000, pp. 47 - 53
Copyright
2000 Cambridge University Press