We introduce the notion of E-ergodicity of a measure-preserving dynamical system (where E is a subset of the natural numbers). We show that given an E-ergodic system T and aperiodic system S, T can be sped up to obtain an isomorphic copy of S, using a function taking values only in E. We give examples applying this concept to the situation where E is a congruence class, the image of an integer polynomial, or the prime numbers.
David M. McClendon
George, Tyler B.
"𝐸-ergodicity and Speedups,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/4