Limiting curves for polynomial adic systems

2017/01/26 by Aleksei Minabutdinov, Minabutdinov, Aleksei
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1701.07617

26 pages,11 figures

arxiv created 2017/01/26 · arxiv updated 2017/01/27

Abstract

We prove the existence and describe limiting curves resulting from deviations in partial sums in the ergodic theorem for cylindrical functions and polynomial (self-similar) adic systems. For a general ergodic measure-preserving transformation and a summable function we give a necessary condition for a limiting curve to exist. Our work generalizes results by É. Janvresse, T. de la Rue and Y. Velenik and answers several questions from their work.

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