Abstract:
We prove the existence of limiting curves (describing deviations in the ergodic theorem) for cylinder functions for 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 E. Janvresse, T. de la Rue, and Y. Velenik.
Key words and phrases:polynomial adic systems, ergodic theorem, deviations in ergodic theorem.