Geometrical Themes Inspired by the N-body Problem

Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera (Herausgeber)

Buch | Softcover

VII, 128 Seiten

2018
Springer International Publishing (Verlag)
978-3-319-71427-1 (ISBN)

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variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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

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).

Erscheinungsdatum	22.03.2018
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	VII, 128 p. 26 illus., 7 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	218 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Arnol'd conjecture for Hamiltonian diffeomorphisms • Complex differential equations • Free homotopy classes of loops • Isochronous solutions • Lagrangian Floer homology • McGehee transformation • Morse Theory • N-Body Problem • Ordinary differential equations
ISBN-10	3-319-71427-9 / 3319714279
ISBN-13	978-3-319-71427-1 / 9783319714271
Zustand	Neuware