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Spatial Recurrence for Ergodic Fractal Measures

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.

preprint2016arXivOpen access
Nadav Dym
math.DS
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