Bi - Invariant Sets and Measureshave Integer Hausdorff
نویسنده
چکیده
Let A; B be two diagonal endomorphisms of the d-dimensional torus with corresponding eigenvalues relatively prime. We show that for any A-invariant ergodic measure , there exists a projection onto a torus T r of dimension r dim , that maps-almost every B-orbit to a uniformly distributed sequence in T r. As a corollary we obtain that the Hausdorr dimension of any bi-invariant measure, as well as any closed bi-invariant set, is an integer.
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