Geometrical Themes Inspired by the N-body Problem

1. Auflage 2018
ISBN: 978-3-319-71427-1
Verlag: Springer

Buch, Englisch, Band 2204, 128 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2175 g

Reihe: Lecture Notes in Mathematics

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variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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

Zielgruppe

Research

Autoren/Hrsg.

Hernández-Lamoneda, Luis

Herrera, Haydeé

Herrera, Rafael

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme

Inhaltsverzeichnis

Preface.- Complex differential equations and geometric structures (Adolfo Guillot). - Blow-up for the N-body problem. Applications to free homotopy type (Richard Motgomery).- A quick view of Lagrangian Floer homology (Andrés Pedroza).