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 17 of 17 for “"diffeomorphisms"”.
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Spaces of diffeomorphisms and embeddings via algebraic K-theory
This thesis comprises two papers that study the homotopy type of spaces of automorphisms and embeddings of high-dimensional manifolds via algebraic K-theory. In the first paper, presented in Chapter 1, we show that the mapping class group is not an h-cobordism invariant of high-dimensional …
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Lyapunov Exponents, Entropy and Dimension
We consider diffeomorphisms of a compact Riemann Surface. 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 …
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Area-contracting maps between rectangles
… on estimating the smallest k-dilation of all diffeomorphisms between two n-dimensional rectangles R and S. I proved that for many rectangles there are highly non-linear diffeomorphisms with much smaller k-dilation than any linear diffeomorphism. When k is equal to n-l, I determined the …
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Large Gauge Transformations and Black Hole Entropy
Diffeomorphisms in general relativity can act non-trivially on the boundary of spacetimes. Of particular importance are the $\textit{BMS group}$ of transformations, originally found by Bondi, Metzner, van der Burg and Sachs. They describe the symmetries of asymptotically flat spacetimes. We first …
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Efficient Numerical Methods for Initial Value Control Problems for Diffeomorphic Image Registration
… Poincaré equations associated with the group of diffeomorphisms. The contributions of this thesis are three-fold: (i) We study the performance of the graphics processing unit implementation of CLAIRE for (large-scale) biomedical imaging studies. (ii) We develop numerical algorithms for the …
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Poisson-lie structures on infinite-dimensional jet groups and their quantization
… Poisson-Lie structures on the group Gy of local diffeomorphisms of the real line R¹ which leave the origin fixed, as well as the extended group of diffeomorphisms G₀<sub>∞</sub> ⊃ G<sub>∞</sub> whose action on R¹ does not necessarily fix the origin. A complete classification of all Poisson-Lie …
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The Fock-Schwartz spin representation space
… actions of the group of orientation-preserving diffeomorphisms, Diff⁺(𝑆¹), and the loop group Spin(2𝑛), as well as the action of an infinite-dimensional Clifford algebra on the Fock-Sobolev spaces and Fock-Schwartz space. All of this work is motivated by the goal of constructing the …
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Partially Hyperbolic Systems: Closed Periodic Curves and Closed Orbits
… study are Anosov flows and partially hyperbolic diffeomorphisms. In recent years, these systems have gained a lot of interest, mainly in dimension 3, where there is lot of machinery available. In the realm of Anosov flows, the orbit structure of these systems plays a major role in understanding …
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Self-adjoint Laplacians and Symmetric Diffusions on Hyperbolic Attractors
… In the special case of partially hyperbolic diffeomorphisms induced by geodesic flows on manifolds of negative sectional curvature the Laplacians we consider are self-adjoint extensions of well-known classical leafwise Laplacians.
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Geometric electroelasticity
… is invariant under the action of arbitrary diffeomorphisms on the surrounding space. This generalizes a result by Marsden and Hughes that pertains to bodies that have the same dimension as the surrounding space and does not allow the presence of electromagnetic fields. Usually, in works on …
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Cosmological Perturbations in the Early Universe
… requires an understanding of how to quantize diffeomorphisms. Deciding on suitable coordinate choices and making sure that this gauge fixing, which is unavoidable in any calculation, does not effect the end result, is tricky. In this thesis we make full use of the effects of diffeomorphism …
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Limiting behavior of Ricci flows
… soliton that we get in the limit is unique up to diffeomorphisms and the convergence toward it is exponential.
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Fluid dynamics in action
… are Stuckelberg-like fields associated with diffeomorphisms and gauge transformations, and are related to the conservation of the stress tensor and a U(1) current if the fluid possesses a charge. This inherently geometric construction gives rise to an emergent "fluid space-time", similar to …
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Magnetic charges and phase space renormalization of gravity
… The Hamiltonian charges corresponding to GBMS diffeomorphisms are non-integrable. We show that the integrable part of these charges faithfully represent the GBMS algebra and in doing so, settle a long-standing open question regarding the existence of infinite-dimensional asymptotic symmetries …
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Studies in Statistical Mechanics and Supersymmetric Lattice Models
… of circle diffeomorphisms, which has gained popularity in recent theoretical physics literature. Its partition function is calculated by the rigorous implementation of an argument by Belokurov and Shavgulidze. This method exploits a regularisation of the …
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SCALABLE MATCHING OF DEFORMED IMAGES
… adaptive Riemannian optimization on the space of diffeomorphisms. We formally quantify the ill-conditioning of deformable registration and develop a novel Eulerian descent formulation enabling powerful adaptive optimization on time-dependent diffeomorphic flows, achieving state-of-the-art …
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Approximating differentiable relationships between delay embedded dynamical systems with radical basis functions
… certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the …