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.
|Commitee:||Connell, Chris, Demeter, Ciprian, Housworth, Elizabeth|
|School Location:||United States -- Indiana|
|Source:||DAI-B 78/03(E), Dissertation Abstracts International|
|Keywords:||Dynamical system, Entropy, Ergodic theory|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be