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Measures of full dimension on affine-invariant sets

Published online by Cambridge University Press:  19 September 2008

R. Kenyon  and
Y. Peres
R. Kenyon
Affiliation:
CNRS UMPA 128, Ecole Normale Superieure de Lyon, 46, allée d'ltalie, 69364 Lyon, France
Y. Peres
Affiliation:
Statistics Department, University of California at Berkeley, Berkeley, CA 94720, USA
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Abstract

We determine the Hausdorff and Minkowski dimensions of some self-affine Sierpinski sponges, extending results of McMullen and Bedford. This result is used to show that every compact set invariant under an expanding toral endomorphism which is a direct sum of conformal endomorphisms supports an invariant measure of full dimension.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 2 , April 1996 , pp. 307 - 323
Copyright
Copyright © Cambridge University Press 1996

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