Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2000. / Includes bibliographical references (p. 59-61).

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 66-68).

This work deals with some aspects of universal topological and metric dynamic behavior of iterated maps of the interval.

Thesis (Ph. D.)--University of Oregon, 2003. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 68-69). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1971. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

M.Sc. (Physics) / The way we live has been fundamentally changed by technological innovations based on optical, electronic and magnetic materials. Without the continuous increase of scienti c understanding on phenomena that occur in materials, together with the processing and synthesis of materials, these technological revolutions would be impossible. Thus, the search of new materials is still the key driving force for the continuous blooming of modern technology...

In this thesis we study descriptive-set-theoretic and measure-theoretic properties of Polish groups, with a thematic emphasis on the contrast between groups which are locally compact and those which are not. The work is divided into three major sections. In the first, working jointly with Robert Kallman, we resolve a conjecture of Gleason regarding the Polish topologization of abstract groups of homeomorphisms. We show that Gleason's conjecture is false, and its conclusion is only true when the hypotheses are considerably strengthened. Along the way we discover a new automatic continuity result for a class of functions which behave like but are distinct from functions of Baire class 1. In the second section we consider the descriptive complexity of those subsets of the permutation group S? which arise naturally from the classical Levy-Steinitz series rearrangement theorem. We show that for any conditionally convergent series of vectors in Euclidean space, the sets of permutations which make the series diverge, and diverge properly, are ?03-complete. In the last section we study the phenomenon of Haar null sets a la Christensen, and the closely related notion of openly Haar null sets. We identify and correct a minor error in the proof of Mycielski that a countable union of Haar null sets in a Polish group is Haar null. We show the openly Haar null ideal may be distinct from the Haar null ideal, which resolves an uncertainty of Solecki. We show that compact sets are always Haar null in S? and in any countable product of locally compact non-compact groups, which extends the domain of a result of Dougherty. We show that any countable product of locally compact non-compact groups decomposes into the disjoint union of a meager set and a Haar null set, which gives a partial positive answer to a question of Darji. We display a translation property in the homeomorphism group Homeo+[0,1] which is impossible in any non-trivial locally compact group. Other related results are peppered throughout.

No presente trabalho iremos provar, usando a folheação de Brouwer-Le Calvez e a teoria de forcing dela derivada, que dado um homeomorfismo f do toro isotópico à identidade tal que seu conjunto de rotação é um segmento de reta com inclinação irracional e tendo 0 como um ponto extremal, então f não possui difusão sublinear na direção perpendicular à direção do conjunto de rotação / In the present work we will prove, using the Brouwer-Le Calvez foliation and the forcing theory derived from it, that given a torus homeomorphism f isotopopic to the identity such that its rotation set is a line segment with irrational slope and 0 is an extreme point, then f does not have sublinear diffusion in the direction perpendicular to the direction of the rotation set.

No presente trabalho apresentamos um estudo sobre a dinâmica de homeomorfismos do toro homotópicos à Dehn twists. No caso conservativo, provamos que se $f$ preserva área e tem um levantamento $\\hat$ para o cilindro com fluxo zero, então, precisamente, ou $f$ é um homeomorfismo do anel, ou possui pontos no cilindro com velocidades verticais positiva e negativa, por iteradas de $\\hat$. Isso resolve a conjectura de Boyland para essa classe de homotopia. Já no caso geral, mostramos um resultado análogo. Além disso, fornecemos uma condição extremamente simples que, quando satisfeita, implica que o conjunto de rotação vertical contém um intervalo e, portanto, que $f$ tem entropia topológica positiva. / The present thesis is concerned with the dynamics of homeomorphisms of the torus homotopic to Dehn twists. We prove that if $f$ is area preserving and it has a lift $\\hat$ to the cylinder with zero flux, then either $f$ is an annulus homeomorphism, or there are points in the cylinder with positive vertical velocity and others with negative vertical velocity, for iterates of $\\hat$. This solves a version of Boyland\'s conjecture to this setting. We extend some theorems we already obtained for Dehn twists with the area preservation hypothesis to a more general class. Finally, we also give a simple explicit condition which, when satisfied, implies that the vertical rotation set contains an interval and thus also implies positive topological entropy.

No presente trabalho apresentamos um estudo sobre a dinâmica de homeomorfismos do toro homotópicos à Dehn twists. No caso conservativo, provamos que se $f$ preserva área e tem um levantamento $\\hat$ para o cilindro com fluxo zero, então, precisamente, ou $f$ é um homeomorfismo do anel, ou possui pontos no cilindro com velocidades verticais positiva e negativa, por iteradas de $\\hat$. Isso resolve a conjectura de Boyland para essa classe de homotopia. Já no caso geral, mostramos um resultado análogo. Além disso, fornecemos uma condição extremamente simples que, quando satisfeita, implica que o conjunto de rotação vertical contém um intervalo e, portanto, que $f$ tem entropia topológica positiva. / The present thesis is concerned with the dynamics of homeomorphisms of the torus homotopic to Dehn twists. We prove that if $f$ is area preserving and it has a lift $\\hat$ to the cylinder with zero flux, then either $f$ is an annulus homeomorphism, or there are points in the cylinder with positive vertical velocity and others with negative vertical velocity, for iterates of $\\hat$. This solves a version of Boyland\'s conjecture to this setting. We extend some theorems we already obtained for Dehn twists with the area preservation hypothesis to a more general class. Finally, we also give a simple explicit condition which, when satisfied, implies that the vertical rotation set contains an interval and thus also implies positive topological entropy.