Overview
- Perfectly suited for young researchers who want to become acquainted with this important field and its open problems
- Contains a very timely exposition of the state of the art on the subject, with an eye to both classical and very recent developments
- Exceptionally well written in a rigorous but also charming style
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2204)
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Table of contents (3 chapters)
Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Geometrical Themes Inspired by the N-body Problem
Editors: Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-71428-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2018
Softcover ISBN: 978-3-319-71427-1Published: 27 February 2018
eBook ISBN: 978-3-319-71428-8Published: 26 February 2018
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VII, 128
Number of Illustrations: 19 b/w illustrations, 7 illustrations in colour
Topics: Dynamical Systems and Ergodic Theory, Calculus of Variations and Optimal Control; Optimization, Ordinary Differential Equations, Geometry, Manifolds and Cell Complexes (incl. Diff.Topology)