Arnold diffusion in the elliptic planar three-body problem

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dc.contributor.authorBakker, Lennard Franken_US
dc.date.accessioned2024-08-13T00:06:11Z
dc.date.available2024-08-13T00:06:11Z
dc.date.copyright1993en_US
dc.date.issued1993
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractIn 1964, V. Arnold conjectured that a chaotic phenomenon, now known as Arnold Diffusion, ex­ists in the three-body problem. In 1993, Z. Xia gave a partial confirmation of the conjecture, showing that Arnold Diffusion exists in the elliptic restricted three-body problem. Xia later generalized his proof to the planar three-body problem. In this thesis, we work towards an understanding of Xia's proof of the existence of Arnold Diffusion in the elliptic restricted three-body problem. The equa­tions of motion of the restricted planar three-body problem are formulated in position-momentum coordinates so that the circular problem is a perturbation of the unperturbed problem, and the el­liptic problem is a perturbation of the circular problem. These equations of motion are transformed in to a form more suited to an analysis of its parabolic solutions. The transformed unperturbed problem is explicitly solved for its parabolic solutions. Under a small enough perturbation from the transformed unperturbed problem to the transformed circular problem, the parabolic solutions of the transformed unperturbed problem are used to give sufficient conditions under which a twist map exists in the discretized transformed circular problem. Under a small enough perturbation from the transformed circular problem to the transformed elliptic problem, KAM Theory is applied to the twist map, near which is then shown the existence of Arnold diffusion.en
dc.format.extent111 pages
dc.identifier.urihttps://hdl.handle.net/1828/17092
dc.rightsAvailable to the World Wide Weben_US
dc.titleArnold diffusion in the elliptic planar three-body problemen_US
dc.typeThesisen_US

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