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ItemPlanar covers of graphs : Negami's conjecture(Georgia Institute of Technology, 1999-08) Hliněnʹy, Petr
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ItemThe effect of stochastic migration on an SIR model for the transmission of HIV(Georgia Institute of Technology, 1999-08) Medlock, Jan P.
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ItemNumerical experiments with models for a particle on a rough inclined plane(Georgia Institute of Technology, 1999-08) Baker, Steven Jeffrey
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ItemColoring girth restricted graphs on surfaces(Georgia Institute of Technology, 1999-08) Walls, Barrett Hamilton
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ItemTopics in airline crew scheduling and large scale optimization(Georgia Institute of Technology, 1999-08) Klabjan, Diego
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ItemIndex pairs : from dynamics to combinatorics and back(Georgia Institute of Technology, 1999-05) Szymczak, Andrzej
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ItemSpectral and asymptotic problems of mathematical physics(Georgia Institute of Technology, 1999) Harrell, Evans M.
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ItemSeveral questions in probability theory(Georgia Institute of Technology, 1999) Hill, Theodore P.
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ItemPersistence of Invariant Tori on Submanifolds in Hamiltonian Systems(Georgia Institute of Technology, 1999) Chow, Shui-Nee ; Li, Yong ; Yi, YingfeiGeneralizing the degenerate KAM theorem under the Rüssmann non-degeneracy and the isoenergetic KAM theorem, we employ a quasi-linear iterative scheme to study the persistence and frequency preservation of invariant tori on a smooth sub-manifold for a real analytic, nearly integrable Hamiltonian system. Under a nondegenerate condition of Rüssmann type on the sub-manifold, we shall show the following: a) the majority of the unperturbed tori on the sub-manifold will persist; b) the perturbed toral frequencies can be partially preserved according to the maximal degeneracy of the Hessian of the unperturbed system and be fully preserved if the Hessian is nondegenerate; c) the Hamiltonian admits normal forms near the perturbed tori of arbitrarily prescribed high order. Under a sub-isoenergetic nondegenerate condition on an energy surface, we shall show that the majority of unperturbed tori give rise to invariant tori of the perturbed system of the same energy which preserve the ratio of certain components of the respective frequencies.
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ItemPersistence of Lower Dimensional Tori of General Types in Hamiltonian Systems(Georgia Institute of Technology, 1999) Li, Yong ; Yi, YingfeiThe work is a generalization to [40] in which we study the persistence of lower dimensional tori of general type in Hamiltonian systems of general normal forms. By introducing a modified linear KAM iterative scheme to deal with small divisors, we shall prove a persistence result, under a Melnikov type of non-resonance condition, which particularly allows multiple and degenerate normal frequencies of the unperturbed lower dimensional tori.