Dissertation/Thesis Abstract

Generalized Boole transformations with infinitely many singularities
by Chen, Yu-Yuan, Ph.D., Indiana University, 2016, 90; 10150137
Abstract (Summary)

George Boole's transformation f(x)=x-1/x is an important example of a Lebesgue measure-preserving transformation of the real line. Generalized Boole transformations with finitely many singularities have been widely studied, and they are known to be measure-preserving, ergodic, conservative, pointwise ergodic, exact, and quasi-finite. We extend this work by considering a certain family of generalized Boole transformations that have infinitely many singularities. We assume that the closure of the set of singularities has Lebesgue measure zero. Transformations in this family are also known to be Lebesgue measure-preserving, and we prove that they are ergodic, conservative, pointwise dual ergodic, exact, and quasi-finite. We find the wandering rates and return sequences of these transformations, and under some further assumptions, we obtain a formula for their entropy. We also investigate the c-isomorphism of these transformations.

Indexing (document details)
Advisor: Gerber, Marlies
Commitee: Connell, Chris, Demeter, Ciprian, Housworth, Elizabeth
School: Indiana University
Department: Mathematics
School Location: United States -- Indiana
Source: DAI-B 78/03(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Mathematics
Keywords: Dynamical system, Entropy, Ergodic theory
Publication Number: 10150137
ISBN: 9781369051780
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