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math.DS2012
On manifolds supporting distributionally uniquely ergodic diffeomorphisms
Artur Avila, Bassam Fayad, Alejandro Kocsard
A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invaria…
math.DS2012
Deviations of ergodic sums for toral translations II. Boxes
Dmitry Dolgopyat, Bassam Fayad
We study the Kronecker sequence on the torus when is uniformly distributed on We show that the discrepancy of the number of…
math.DS2012
Deviations of Ergodic sums for Toral Translations I : Convex bodies
Dmitry Dolgopyat, Bassam Fayad
We show the existence of a limiting distribution $\cD_\cC$ of the adequately normalized discrepancy function of a random translation on a torus relative to a strictly convex set $\…