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Geometrical Themes Inspired by the N-body Problem

  • Luis Hernández-Lamoneda
  • Haydeé Herrera
  • Rafael Herrera

Part of the Lecture Notes in Mathematics book series (LNM, volume 2204)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Andrés Pedroza
    Pages 91-125
  3. Back Matter
    Pages 127-128

About this book

Introduction

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variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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

Keywords

N-body problem Complex differential equations Isochronous solutions Free homotopy classes of loops McGehee transformation Lagrangian Floer homology Arnol'd conjecture for Hamiltonian diffeomorphisms Morse theory

Editors and affiliations

  • Luis Hernández-Lamoneda
    • 1
  • Haydeé Herrera
    • 2
  • Rafael Herrera
    • 3
  1. 1.Department of MathematicsMathematics Research Center (CIMAT)GuanajuatoMexico
  2. 2.Department of MathematicsRutgers UniversityCamden, NJUSA
  3. 3.Department of MathematicsMathematics Research Center (CIMAT)GuanajuatoMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-71428-8
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-71427-1
  • Online ISBN 978-3-319-71428-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site