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.

Author Bio

Tyler George completed this research while working on his Bachelors of Science in Applied Mathematics at Ferris State University. He worked closely with Dr. David McClendon in the field of dynamical systems and eventually specifically ergodic theory. This work contributed to both a presentation and a formal poster on the topics of this paper. Tyler recognizes this research and other work with his mentor Dr. McClendon was the single most important experience of his undergraduate studies. Tyler has completed one year towards his master degree but plans on continuing until he completes his PhD in mathematics with a concentration in the teaching of college mathematics at Central Michigan University.