Geometrical themes inspired by the N-body problem / Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera, editors
Type de document : MonographieCollection : Lecture notes in mathematics, 2204Langue : anglais.Pays: Swisse.Éditeur : Cham : Springer, 2018Description : 1 vol. (VII-125 p.) : ill. ; 24 cmISBN: 9783319714271.ISSN: 0075-8434.Bibliographie : Bibliogr. en fin de contributions.Sujet MSC : 53-06, Proceedings, conferences, collections, etc. pertaining to differential geometry70F07, Dynamics of a system of particles, including celestial mechanics, Three-body problems
37J46, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Periodic, homoclinic and heteroclinic orbits
53C15, Global differential geometry, General geometric structures on manifolds
53D12, Differential geometry - Symplectic geometry, contact geometry, Lagrangian submanifolds; Maslov indexEn-ligne : ZbMath | MSN | Springer
| Item type | Current library | Call number | Status | Date due | Barcode |
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Monographie
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CMI Salle 1 | 53-06 HER (Browse shelf(Opens below)) | Available | 12499-01 |
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from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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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