Spatial Recurrence for Ergodic Fractal Measures

2016/02/09 by Nadav Dym, Dym, Nadav
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1602.02894

arxiv created 2016/02/09 · arxiv updated 2016/02/10

Abstract

We discuss an invertible version of Furstenberg's `Ergodic CP Shift Systems'. We show that the explicit regularity of these dynamical systems with respect to magnification of measures, implies certain regularity with respect to translation of measures; We show that the translation action on measures is non-singular, and prove pointwise discrete and continuous ergodic theorems for the translation action.

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