Hawkins, Jane M. (1980) Type III diffeomorphisms of manifolds. PhD thesis, University of Warwick.

Preview

PDF WRAP_Theses_Hawkins_1980.pdf - Submitted Version - Requires a PDF viewer. Download (4Mb) | Preview

Request Changes to record.

Abstract

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.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Diffeomorphisms, Manifolds (Mathematics), Ergodic theory
Official Date:	1980
Dates:	Date Event 1980 UNSPECIFIED
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Schmidt, Klaus, 1943-
Extent:	x, 105 leaves
Language:	eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads