dc.contributor.advisor Schaad, Beat dc.contributor.author Sofiani, Majed dc.date.accessioned 2018-01-30T03:46:26Z dc.date.available 2018-01-30T03:46:26Z dc.date.issued 2017-05-31 dc.date.submitted 2017 dc.identifier.other http://dissertations.umi.com/ku:15285 dc.identifier.uri http://hdl.handle.net/1808/25828 dc.description.abstract In this work, we will be investigating a specific Hamiltonian system, namely, the Kepler problem with a correction term $\frac{\delta}{r^{3}}$ added to the potential energy. Our objective is to show that the system is stable in the sense of the KAM theorem. In the first sections, we introduce essential concepts and tools that will be used in the process of understanding and showing how the KAM theorem works with our system. These concepts and tools are: Hamiltonian formalism, canonical transformations, the Hamilton-Jacobi equation and Action-Angle variables. In the last section, we state the KAM theorem and, based on the results we obtain from previous sections, we can conclude that the system is in fact stable in the sense of the KAM theorem. An informal statement of the KAM theorem is that if the unperturbed Hamiltonian system $H_{0}$, expressed in the action variable $J$, is non-degenerate, then under sufficiently small perturbation $\epsilon H_{1}$ we have that \begin{equation*}\label{pert} H(J,\Phi)=H_{0}(J)+\epsilon H_{1}(J,\Phi) \end{equation*} for $\epsilon 0$. dc.format.extent 61 pages dc.language.iso en dc.publisher University of Kansas dc.rights Copyright held by the author. dc.subject Mathematics dc.subject Action-Angle variables dc.subject General relativity dc.subject KAM theorem dc.subject Kepler Problem dc.title KAM Stability of The Kepler Problem with a General Relativistic Correction Term dc.type Thesis dc.contributor.cmtemember Stefanov, Atanas dc.contributor.cmtemember Stanislavova, Milena dc.thesis.degreeDiscipline Mathematics dc.thesis.degreeLevel M.A. dc.identifier.orcid dc.rights.accessrights openAccess
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