Thesis (Master)--İzmir Institute of Technology, İzmir, 2005 / Keywords: Nonlinear differential equations, finite difference method, numeric simulation. Includes bibliographical references (leaves. 55-57).

In this dissertation we study the anisotropic Manev problem that describes the motion of two point masses in an anisotropic space under the influence of a Newtonian force-law with a relativistic correction term. The dynamic of the system under discussion is very complicated and we use various methods to find a qualitative description of the flow. One of the strategies we use is to study the collision and near collision orbits. In order to do that we utilize McGehee type transformations that lead to an equivalent analytic system with an analytic energy relation. In these new coordinates the collisions are replaced by an analytic two-manifold: the so called collision manifold. We focus our attention on the heteroclinic orbits connecting fixed points on the collision manifold and on the homoclinic orbit to the equator of the mentioned manifold. We prove that as the anisotropy is introduced only four heteroclinic orbits persist and we show the exixtence of infinitely many transversal homoclinic orbits using a suitable generalization of the Poincaré-Melnikov method. Another strategy we apply is to study the symmetric periodic orbits of the system. To tackle this problem we follow two different approaches. First we apply the Poincaré continuation method and we find symmetric periodic orbits for small values of the anisotropy. Then we utilize a direct method of the calculus of variations, namely the lower semicontinuity method, and we prove the existence of symmetric periodic orbits for any value of the anisotropy parameter. In the last chapter we use the Killing's equation in an unusual way to prove that the anisotropic Kepler problem (that can be considered a particular case of the Manev) does not have first integrals linear in the momentum. / Graduate

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (February 28, 2007) Vita. Includes bibliographical references.

published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis--Princeton University. / Cover title. "Reprinted from the Transactions of the American Mathematical Society, vol. 62, no. 3 ... November, 1947." Bibliography: p. 386.

Thesis (Ph. D.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 123-125). Also available via the World Wide Web.

Thesis (M. Phil.)--University of Hong Kong, 1995. / Includes bibliographical references (leaves 83-86).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Vita. Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Delaware, 1997. / Includes bibliographical references (leaves 181-190).