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＜E-Book＞
Geometrical Themes Inspired by the N-body Problem / edited by Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera
(Lecture Notes in Mathematics. ISSN:16179692 ; 2204)

Edition	1st ed. 2018.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2018
Language	English
Size	VII, 128 p. 26 illus., 7 illus. in color : online resource
Authors	Hernández-Lamoneda, Luis editor Herrera, Haydeé editor Herrera, Rafael editor SpringerLink (Online service)
Subjects	LCSH:Dynamical systems LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations LCSH:Geometry LCSH:Manifolds (Mathematics) FREE:Dynamical Systems FREE:Calculus of Variations and Optimization FREE:Differential Equations FREE:Geometry FREE:Manifolds and Cell Complexes
Notes	Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot’s notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions.   R. Montgomery’s notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of theapproach is the use of energy-balance in order to motivate the McGehee transformation.    A. Pedroza’s notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol’d conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism HTTP:URL=https://doi.org/10.1007/978-3-319-71428-8

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