Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 22 for “"ergodic theory"”.
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Convergence in Ergodic Theory
… two problems involving convergence in ergodic theory. The first problem is the following: Given a measure preserving transformation T and a weight function w(alpha) → 0 as alpha → 0, is there a p > 0 such that the expression w(alpha)#{ n : 1n k=1nfT kx >a } have a limit, a.s. …
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Divergence in Ergodic Theory
Let (X, B , P) be a non-atomic probability space and let T be an invertible measure-preserving transformation of ( X, B , P). Fix a sequence (mk ) in Z and let f ∈ Lp( X), 1 ≤ p ≤ infinity. We know that, depending on what the powers are, the averages 1n k=1nfTmk x may or may not converge …
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H(p) Spaces and Inequalities in Ergodic Theory
This thesis combines the theory of ergodic Hp spaces, singular integral operators and the theory of Banach space-valued operators to establish a new method to study the inequalities for the operators induced by an ergodic, measure preserving transformation. This method also indicates the close …
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Philosophical aspects of chaos: definitions in mathematics, unpredictability, and the observational equivalence of deterministic and indeterministic descriptions
… I examine notions of unpredictability in ergodic theory, and I ask what they tell us about the justification and formulation of mathematical definitions. The main account of the actual practice of justifying mathematical definitions is Lakatos's account on proof-generated definitions. By …
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Centralizers in automorphism groups
… chapter, we discuss the centralizer question in ergodic theory, an open question that has served as motivation for much of the work in this dissertation. We also introduce the content of each of the subsequent chapters and describe how it relates to the centralizer question in ergodic theory. In …
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Theory of large quantal systems and the quantum theory of measurement
… and Prosperi, based on a time-independent ergodic theory of large quantal systems; the other by the Belgian group of George, Prigogine and Rosenfeld, based on a time-dependent theory. In this thesis these two theories are compared and are shown to be equivalent.
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Topological Dynamics of Automorphism Groups of omega-homogeneous Structures via Near Ultrafilters
… of structures and structural Ramsey theory from countable to uncountable structures. This allows us to provide new examples of explicit descriptions of universal minimal flows as well as of extremely amenable groups. We identify new classes of finite structures satisfying the Ramsey …
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Thermodynamical Formalism
… The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressure and measure …
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Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms
… the foundations of statistical mechanics through ergodic theory. This putative connection is made more concrete in Part I of this thesis, where we show how to quantify certain chaotic properties of a system that are of relevance to statistical mechanics and kinetic theory. We consider the motion …
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Applications of dynamical systems to Farey sequences and continued fractions
… explores three main topics in the application of ergodic theory and dynamical systems to equidistribution and spacing statistics in number theory. The first is concerned with utilizing the ergodic properties of the horocycle flow in SL(2,R) to study the spacing statistics of Farey fractions. For a …
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Arithmetic Structure in Sets of Integers
… discuss the connections with recent results in ergodic theory. Chapter 3 deals with improved upper and lower bounds on the minimum number of monochromatic 4-term progressions in any two-colouring of ZN. Finally, in Chapter 4 we investigate the structure of the set of popular di erences of a …
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Price formation under uncertainty
… e.g. rational expectations hypothesis versus the theory of rational beliefs. Accordingly, empirical evidence is presented to support analyses of models in which agents are not assumed to have structural knowledge. Simple general equilibrium models are used to illustrate that modelling risk …
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Theoretical foundations for finite-time transient stability and sensitivity analysis of power systems
… analysis of power systems, based on the theory of normally hyperbolic invariant manifolds and finite time Lyapunov exponents, adopted from geometric theory of dynamical systems. The theory of normally hyperbolic surfaces allows us to characterize the rate of expansion and contraction of …
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Coloring problems in combinatorics and descriptive set theory
… context and in the framework of descriptive set theory, with applications to topological dynamics and ergodic theory. This work consists of two parts, each of which is in turn split into a number of chapters. Although the individual chapters are largely independent from each other (with the …
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Cubulating CAT(0) groups and Property (T) in random groups
… (T) has had an impact on areas such as group theory, ergodic theory, and expander graphs. The aim is to cubulate some examples of groups known in the literature, and prove that many ‘generic’ groups have Property (T). Graphs will be central objects of study throughout this text, and so in …
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Pointwise ergodic theorems via descriptive set theory
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2024-05-01
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d-bar continuity beyond subshifts of finite type
… this proof was the $\overline{d}$-metric. Many ergodic properties are well-behaved with respect to this metric. The entropy function $\mu \mapsto h_{\mu}(\sigma)$ is $\overline{d}$-continuous. Moreover, the set of processes that are isomorphic to Bernoulli shifts is $\overline{d}$-closed. The …
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Geometric and ergodic properties of certain classes of continued fractions
Made available in DSpace on 2019-11-26T20:33:47Z (GMT). No. of bitstreams: 2 MERRIMAN-DISSERTATION-2019.pdf: 3545539 bytes, checksum: 1ceb6dccbf49a654427e8d1f15d2be3d (MD5) LICENSE.txt: 4212 bytes, checksum: b6441bf949f57dfb6f36245b79c18128 (MD5) Previous issue date: 2019-07-08
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Lyapunov Exponents, Entropy and Dimension
… A development of Oseledec's Multiplicative Ergodic Theorem is given, along with a development of measure theoretic entropy and dimension. The main result, due to L.S. Young, is that for certain diffeomorphisms of a surface, there is a beautiful relationship between these three concepts; …
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