In this dissertation we investigate the following problem in ergodic theory: Let X be a Polish space and T:X→X a homeomorphism. We ask whether there exists a non-atomic Borel probability measure m on X, ergodic and quasi-invariant under T, such that the cohomology class of some preassigned continuous function f:X→S1 is trivial. The cohomology class of f is trivial and f is called a coboundary of T, if the equation hTx=f x˙hx m-almosteverywhere admits a measurable solution h:X→S1 In the presence of a non-periodic recurrent point x0∈X , we establish the existence of such a measure m . Indeed, our approach, which is based on a construction of Katznelson and Weiss, yields a continuum of such measures all of which are of type IIinfinity and pointwise orthogonal. And the same statement is true for measures of type III / acase@tulane.edu
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_25944 |
| Date | January 1999 |
| Contributors | Rothe, Magnus (Author), Riedel, Norbert (Thesis advisor) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Rights | Access requires a license to the Dissertations and Theses (ProQuest) database., Copyright is in accordance with U.S. Copyright law |
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