Entropy of Transformations that Preserve an Infinite Measure

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Bayless, Rachel Louise
- Affiliation: College of Arts and Sciences, Department of Mathematics

Abstract

In this dissertation we study transformations that preserve an infinite measure, with a focus on functions which preserve Lebesgue measure on the real line. More specifically, we investigate measure-theoretic properties of rational R-functions of negative type. We prove all rational R-functions of negative type are conservative, exact, ergodic, rationally ergodic, pointwise dual ergodic, and quasi-finite. We also explicitly construct the wandering rates and return sequences for all rational R-functions of negative type. The primary topic of study, however, is entropy of transformations preserving an infinite measure. We provide a method of computing the Krengel entropy for all rational R-functions of negative type. We also provide complete isomorphism invariants for c-isomorphisms between degree two rational R-functions of negative type.

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