Infinite-Dimensional Dynamical Systems and Projections

In this dissertation we study an algorithm for convex optimization problems in conic form. (Without loss of generality, any We address three problems arising in the theory of infinite-dimensional dynamical systems. First, we study the extent to which the Hausdorff dimension and the dimension spectrum of a fractal measure supported…


1 Introduction
2 Projections of Fractal Sets and Measures
2.1 Introduction
2.2 Preliminaries
2.2.1 Prevalence
2.2.2 The Dimension Spectrum
2.2.3 The Thickness Exponent
2.3 Main Results
2.4 Nonpreservation of Hausdorff Dimension
3 The Viscous Lake Equations
3.1 Introduction
3.2 The Shallow Water Model
3.3 The Attractor
3.3.1 Absorbing Set in H
3.3.2 Absorbing Set in V
3.4 Upper Bound on the Attractor Dimension
3.4.1 Uniform Lyapunov Exponents
3.4.2 The Estimate
3.5 The Weighted Lieb-Thirring Inequality
4 Learning About Reality From Observation
4.1 Introduction
4.1.1 The case of linear f and φ
4.1.2 What does “typical” mean?
4.1.3 Overview of this paper
4.1.4 The Transference Method
4.2 Prevalence
4.2.1 Cardinality Preservation
4.2.2 Preservation of Unboundedness
4.3 Enveloping Manifolds
4.4 Platonic Embedology
4.5 Observing A Continuous Dynamical System….


Author: Ott, William Raymond

Source: University of Maryland

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