Limiting Curves for Polynomial Adic Systems

Abstract

We prove the existence of and describe limiting curves resulting from deviations in the partial sums in the ergodic theorem for cylinder functions and polynomial 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.