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Title: Type III diffeomorphisms of manifolds
Author: Hawkins, Jane M.
ISNI:       0000 0001 3547 1003
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1980
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This thesis is about a classification of ergodic diffeomorphisms of manifolds introduced by Krieger. We start with the definition which states that if f denotes a non-singular ergodic transformation of a probability space (X,S,u) which admits no o-finite invariant measure equivalent to the given measure, then f is of type III. We then look at a finer division of the type III class of transformations by specifying the ratio set of f, which gives information about the values that the Radon-Nikodym derivative of fn (the n /th iterate of f) takes on sets of positive measure. The ratio set is an invariant of weak equivalence, hence of conjugation by diffeomorphisms. We examine some relationships between the differentiable and metric structures of diffeomorphisms of manifolds, starting with some known results on the circle. The first chapter introduces most of the necessary definitions, background theorems, and notation. The second chapter extends results of Herman and Katznelson by giving 2 a construction for C2 diffeomorphisms of the circle which are of type 111. The rotation numbers of these diffeomorphisms form a set of measure 1 in [0,l]; Herman's theorem shows this is not possible for C3 diffeomorphisms.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics