Second Order Ergodic Theorem for Self-Similar Tiling Systems

2012/09/18 by Konstantin Medynets, Medynets, Konstantin, Boris Solomyak +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1209.4073

Text improved. Typos Fixed

arxiv created 2013/03/18 · arxiv updated 2013/03/19

Abstract

We consider infinite measure-preserving non-primitive self-similar tiling systems in Euclidean space \mathbb R^d. We establish the second-order ergodic theorem for such systems, with exponent equal to the Hausdorff dimension of a graph-directed self-similar set associated with the substitution rule.

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