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A new information cocycle with some applications
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Butler, Roger Anthony Roy (1982) A new information cocycle with some applications. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3231224~S15
Abstract
The primary aim of this thesis is to present an information cocycle for groups of non-singular transformations.
In Section 1 we produce some coding results for Lipschitz partitions that are later used to associate canonically an Information cocycle to Axiom A* homeomorphisms.
As a specific example of the use of coding techniques, in Section 2 we prove that a Markov shift over finitely many states is isomorphic to its inverse, by a finitary isomorphism with finite expected code lengths. We also show that reversibility is a generic property.
In Section 3, an information cocycle is defined for groups of non-singular transformations. Some of Its properties are then investigated, including its close relation to entropy, and an application is presented.
The information cocycle for single non-singular transformations is considered in Section 4, where we also study several conditions that imply that two σ-algebras are I-related.
In Section 5, the form of the information cocycle is calculated for generalised Markov shifts, and finite co-ordinate changes on shift spaces. Some invariants of the information cocycle-coboundary equation are also produced.
Section 6 contains two constructions for producing ergodic non-singular Bernoulli measures that are not equivalent to shift invariant probability measures.
| Item Type: | Thesis or Dissertation (PhD) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Cocycles, Transformations (Mathematics), Ergodic theory | ||||
| Official Date: | July 1982 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Mathematics Institute | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Schmidt, Klaus, 1943- | ||||
| Sponsors: | Science Research Council (Great Britain) | ||||
| Format of File: | |||||
| Extent: | v, 179 leaves | ||||
| Language: | eng |
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