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Regularization of kepler's problem and the averaging method on a manifold
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This article is published in Communications on Pure and Applied Mathematics.The article was published on 1970-07-01. It has received 466 citations till now. The article focuses on the topics: Regularization (mathematics) & Method of averaging.read more
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Triple collision in the collinear three-body problem.
TL;DR: This paper is concerned with Singularity (regularization) and regularization (singularity) in the 21st Century, specifically the aftermath of 9/11.
Book
Hamiltonian Reduction by Stages
TL;DR: Marsden, Jerrold E. Marsden as discussed by the authors proposed a reduction theory for Symplectic Geometry (Math-ematics) based on the Hamiltonian reduction by stages (Springer Lecture Notes in Mathematics).
Journal ArticleDOI
Critical points and nonlinear variational problems
Abstract: This monograph deals with critical point theory and its applications to some classes of nonlinear variational problems. The abstract setting includes the Lusternik-Schnirelman theory and minimax methods for unbounded functionals. Applications to elliptic boundary value problems, Vortex theory, homoclinic orbits and conservative systems with singular potentials are discussed. Resume. Cette monographic traite de la theorie des points critiques et de ses applications a quelques classes de problemes variationels non lineaires. Le cadre abstrait comprend la theorie de Lusternik-Schnirelman et les methodes de minimax pour des fonctionelles non bomees. Nous examinons des applications a la theorie des problemes aux limites elliptiques, a celle du vortex, aux orbites homocliniques, et aux systemes conservatifs avec potentiels singuliers. (*) Texte recu le 13 d6cembre 1991 A. Ambrosetti, Scuola Normale Superiore, Piazza dei Cavalieri 56 100 Pisa, Italic
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Topology from the differentiable viewpoint
TL;DR: The fundamental theorem of algebra and its application to smooth manifolds and smooth maps was proved by Sard and Brown as discussed by the authors, and the Brouwer degree modulo 2 of a mapping was shown to be equivalent to the Hopf theorem.
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Perturbation theory of Kepler motion based on spinor regularization.
E. Stiefel,P. Kustaanheimo +1 more
TL;DR: In this article, Kustaanheimo et al. developed a regularization of Kepler motion using a simple mapping of a four-dimensional space R* onto a 3D space Ä, where the equations of any undisturbed Kepler motion are linear differential equations.