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dc.contributor.authorLu, Nanen_US
dc.date.accessioned2011-09-22T17:48:09Z
dc.date.available2011-09-22T17:48:09Z
dc.date.issued2011-05-18en_US
dc.identifier.urihttp://hdl.handle.net/1853/41090
dc.description.abstractIn this thesis, we study the normally elliptic singular perturbation problems including both finite and infinite dimensional cases, which could also be non-autonomous. In particular, we establish the existence and smoothness of O(1) local invariant manifolds and provide various estimates which are independent of small singular parameters. We also use our results on local invariant manifolds to study the persistence of homoclinic solutions under weakly dissipative and conservative per- turbations. We apply Semi-group Theory and Lyapunov-Perron Integral Equations with some careful estimates to handle the O(1) driving force in the system so that we can approximate the full system through some simpler limiting system. In the investigation of homoclinics, a diagonalization procedure and some normal form transformation should be first carried out. Such diagonalization procedure is not trivial at all. We discuss this issue in the appendix. We use Melnikov type analysis to study the weakly dissipative case, while the conservative case is based on some energy methods. As a concrete example, we have shown rigrously the persistence of homoclinic solutions of an elastic pendulum model which may be affected by damping, external forcing and other potential fields.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectDynamical systemen_US
dc.subjectInvariant manifolden_US
dc.subjectHomoclinic orbiten_US
dc.subject.lcshPerturbation (Mathematics)
dc.subject.lcshSingular perturbations (Mathematics)
dc.titleNormally elliptic singular perturbation problems: local invariant manifolds and applicationsen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Member: Chow, Shui-Nee; Committee Member: Dieci, Luca; Committee Member: Huo, Xiaoming; Committee Member: Lin, Zhiwu; Committee Member: Pan, Ronghua; Committee Member: Zeng, Chongchunen_US


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