Ergodic Theory and Dynamical Systems

Research Article

Measures of full dimension on affine-invariant sets

R. Kenyona1 and Y. Peresa2

a1 CNRS UMPA 128, Ecole Normale Superieure de Lyon, 46, allée d'ltalie, 69364 Lyon, France

a2 Statistics Department, University of California at Berkeley, Berkeley, CA 94720, USA


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.

(Received October 14 1993)

(Revised June 20 1994)