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Cosmologia e o principio de Maupertuis-Jacobi / Cosmology and the Maupertuis-Jacobi principleElias, Luciana Aparecida 14 March 2008 (has links)
Orientador: Alberto Vazquez Saa / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-09-24T19:33:36Z (GMT). No. of bitstreams: 1
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Previous issue date: 2008 / Resumo: Mostraremos que as equações de movimento de uma classe de modelos cosmológicos anisotrópicos envolvendo campos escalares com acoplamento não mínimo à gravitação são equivalentes ao fluxo geodésico em certas variedades estendidas munidas de uma métrica não-riemanniana, generalizando alguns trabalhos recentes e permitindo uma melhor classificação dinâmica do espaço de fase das soluções destes modelos cosmológicos. Essencialmente, as técnicas empregadas neste trabalho são uma generalização do conhecido Princípio de Maupertuis-Jacobi da Mecânica Clássica, o qual permite associar o fluxo geodésico de uma métrica particular (a métrica de Jacobi) às equações de movimento de um dado sistema mecânico, tipicamep.te Hamiltoniano. Mostraremos também que a abordagem geométrica baseada na métrica de Eisenhart da mecânica clássica pode ser generalizada de maneira análoga ao do Princípio de Maupertuis-Jacobi para o caso de equações cosmológicas, permitindo a introdução de um outro enfoque geométrico complementar àquele correspondente à generalização' do Princípio de Maupertuis-Jacobi. Estes resultados são aplicados a modelos cosmológicos de quintessência atuais e resultados interessantes e promissores são obtidos / Abstract: We will show that the equations of motion for a class of non-minimally coupled anisotropic scalar-tensorial cosmological models are equivalent to the geodesic fux on certain augmented manifold endowed with a non-Riemannian metric. This result generalizes some recent ones and provides a better dynamical classification of the phase space of such cosmological models. The
techniques employed in this work are, basically, a generalization of the well known Maupertuis- Jacobi Principle of Classical Mechanics, which allows us to associate the geodesic flux of a particular metric (the so called Jacobi Metric) to the equations of motion of a given mechanical system, typically a Hamiltonian one. We will show also that the classical geometrical approach based on the Eisenhart metric can be generalized in an analogous way for the cosmological case, leading to another complementary geometrical approach to that one corresponding to the generalization of the Maupertuis-Jacobi Principle. Such results are applied to certain quintessential cosmological models leading to some interesting and promising results / Doutorado / Fisica-Matematica / Doutor em Matemática Aplicada
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Um estudo sobre incompletude de geodésicas semi-Riemannianas / A study on uncompleteness of semi-Riemannian geodesicsNunes, Lucas de Faccio 15 August 2019 (has links)
Nesse trabalho apresentaremos alguns exemplos clássicos que evidenciam as diferenças entre a geometria Riemanniana e a semi-Riemanniana (Lorentziana) quanto à completude de geodésicas. Para isso, revisitaremos conceitos básicos de Geometria, seguido de uma introdução aos espaços vetoriais de Lorentz e um estudo inicial sobre o grupo de Lorentz. Nos capítulos finais discutiremos sobre completude de geodésicas e como se distanciam do caso Riemanniano. / In this work we intend to present some classical examples that display the differences between Riemannian and semi-Riemannian (Lorentzian) geometry in relation to the completeness of geodesics. For this, we will revisit basic Geometry concepts followed by an introduction to the vector spaces of Lorentz and a simple study on the Lorentz group. In the final chapters we will discuss about the completeness of geodesics and how it distances itself from the Riemannian case.
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The Markoff spectrum and geodesics on the punctured torus / David J. Crisp.Crisp, David J. January 1993 (has links)
Bibliography : leaves 184-188. / vi, 188 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.)--University of Adelaide, Dept. of Pure Mathematics, 1994
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Sur une nouvelle méthode pour le calcul des perturbations du mouvement des planètes Sur les propriétés des lignés géodésiques /Saint Loup, Jean François Louis. January 1900 (has links)
Thèse de doctorat : Astronomie : Paris, Faculté des sciences : 1857. Thèse de doctorat : Géométrie : Paris, Faculté des sciences : 1857. / Titre provenant de l'écran-titre.
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Evolutionary computation of geodesic paths in CAD/CAMXue, Feng, 薛峰 January 2001 (has links)
published_or_final_version / Industrial and Manufacturing Systems Engineering / Master / Master of Philosophy
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The gravitational lens effect of galaxies and black holes / by Igor BrayBray, Igor January 1986 (has links)
Bibliography: leaves 122-123 / iii, 123 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Mathematical Physics, 1986
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The gravitational lens effect of galaxies and black holes /Bray, Igor. January 1986 (has links) (PDF)
Thesis (Ph. D.)--University of Adelaide, Dept. of Mathematical Physics, 1986. / Includes bibliographical references (leaves 122-123).
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A support theorem and an inversion formula for the geodesic ray transform /Krishnan, Venkateswaran P., January 2007 (has links)
Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 51-56).
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Regularity of ghosts of geodesic X-ray transform /Skokan, Michal. January 2004 (has links)
Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 61-63).
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Reconstructing and analyzing surfaces in 3-spaceSun, Jian, January 2007 (has links)
Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 129-135).
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