Entropy of Transformations that Preserve an Infinite Measure Public Deposited

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  • March 22, 2019
Creator
  • 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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  • In Copyright
Advisor
  • Hawkins, Jane
Degree
  • Doctor of Philosophy
Graduation year
  • 2013
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