Geometrical themes inspired by the N-body problem / Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera, editors

Auteur secondaire : Hernández-Lamoneda, Luis - Editeur scientifique ; Herrera, Haydeé - Editeur scientifique ; Herrera, Rafael - Editeur scientifiqueType de document: MonographieCollection: Lecture notes in mathematics ; 2204Langue: anglaisPays: SwisseÉditeur: Cham : Springer, 2018Description: 1 vol. (VII-125 p.) : ill. ; 24 cm ISBN: 9783319714271 ; br. ISSN: 0075-8434Note: Textes issus de trois mini-cours donnés lors du 7e "Mini-meeting on differential geometry", tenu au Center for research in mathematics (CIMAT) de Guanajuato, Mexico, 17-19 février 2015Résumé: Publisher’s description: 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from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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 the approach 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..Bibliographie: Bibliogr. en fin de contributions. Sujets MSC: 53-06 Differential geometry -- Proceedings, conferences, collections, etc
70F07 Mechanics of particles and systems -- Dynamics of a system of particles, including celestial mechanics -- Three-body problems
37J45 Dynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems -- Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
53C15 Differential geometry -- Global differential geometry -- General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D12 Differential geometry -- Symplectic geometry, contact geometry -- Lagrangian submanifolds; Maslov index
En-ligne: ZbMath | MSN | Springer
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Textes issus de trois mini-cours donnés lors du 7e "Mini-meeting on differential geometry", tenu au Center for research in mathematics (CIMAT) de Guanajuato, Mexico, 17-19 février 2015

Bibliogr. en fin de contributions

Publisher’s description: 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 the approach 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.

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