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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

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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:
DateEvent
July 1982Submitted
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Publication Status: Unpublished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: pdf
Extent: v, 179 leaves
Language: eng

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