Geometrical Themes Inspired by the N-body Problem

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Hernández-Lamoneda, Luis (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Herrera, Haydeé (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Herrera, Rafael (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Lecture Notes in Mathematics, 2204
• Θέματα: Dynamics.; Ergodic theory.; Calculus of variations.; Differential equations.; Geometry.; Manifolds (Mathematics).; Complex manifolds.; Dynamical Systems and Ergodic Theory.; Calculus of Variations and Optimal Control; Optimization.; Ordinary Differential Equations.; Manifolds and Cell Complexes (incl. Diff.Topology).

 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from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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.