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Hamiltonian systems and the calculus of differential forms on the Wasserstein spaceKim, Hwa Kil. January 2009 (has links)
Thesis (Ph.D)Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Gangbo, Wilfrid; Committee Member: Loss, Michael; Committee Member: Pan, Ronghua; Committee Member: Swiech, Andrzej; Committee Member: Tannenbaum, Allen. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Hamiltonian methods in weakly nonlinear VlasovPoisson dynamics /Yudichak, Thomas William, January 2001 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 115121). Available also in a digital version from Dissertation Abstracts.

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Resonance overlap, secular effects and nonintegrability: an approach from ensemble theoryLi, Chun Biu 28 August 2008 (has links)
Not available / text

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State space relativity : an analysis of relativity from the Hamiltonian point of viewLow, Stephen G. January 1982 (has links)
No description available.

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From commutators to halfforms : quantisationRoberts, Gina January 1987 (has links)
No description available.

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Hamiltonian cycle problem, Markov decision processes and graph spectraNguyen, Giang Thu January 2009 (has links)
The Hamiltonian cycle problem (HCP) can be succinctly stated as: "Given a graph, find a cycle that passes through every single vertex exactly once, or determine that this cannot be achieved". Such a cycle is called a Hamiltonian cycle. The HCP is a special case of the better known Travelling salesman problem, both of which are computationally difficult to solve. An efficient solution to the HCP would help solving the TSP effectively, and therefore would have a great impact in various fields such as computer science and operations research. In this thesis, we obtain novel theoretical results that approach this discrete, deterministic, problem using tools from stochastic processes, matrix analysis, and graph theory. / PhD Doctorate

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Resonance overlap, secular effects and nonintegrability an approach from ensemble theory /Li, Chun Biu, January 2003 (has links) (PDF)
Thesis (Ph. D.)University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

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State space relativity : an analysis of relativity from the Hamiltonian point of viewLow, Stephen G. January 1982 (has links)
No description available.

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From commutators to halfforms : quantisationRoberts, Gina January 1987 (has links)
No description available.

20 
Hamiltonian systems and the calculus of differential forms on the Wasserstein spaceKim, Hwa Kil 01 June 2009 (has links)
This thesis consists of two parts. In the first part, we study stability properties of Hamiltonian systems on the Wasserstein space. Let H be a Hamiltonian satisfying conditions imposed in the work of Ambrosio and Gangbo. We regularize H via MoreauYosida approximation to get H[subscript Tau] and denote by μ[subscript Tau] a solution of system with the new Hamiltonian H[subscript Tau] . Suppose H[subscript Tau] converges to H as τ tends to zero. We show μ[subscript Tau] converges to μ and μ is a solution of a Hamiltonian system which is corresponding to the Hamiltonian H. At the end of first part, we give a sufficient condition for the uniqueness of Hamiltonian systems. In the second part, we develop a general theory of differential forms on the Wasserstein space. Our main result is to prove an analogue of Green's theorem for 1forms and show that every closed 1form on the Wasserstein space is exact. If the Wasserstein space were a manifold in the classical sense, this result wouldn't be worthy of mention. Hence, the first cohomology group, in the sense of de Rham, vanishes.

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