Geometrical Themes Inspired by the N-body Problem: Lecture Notes in Mathematics, cartea 2204
Editat de Luis Hernández-Lamoneda, Haydeé Herrera, Rafael Herreraen Limba Engleză Paperback – 27 feb 2018
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from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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.
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.
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Specificații
ISBN-13: 9783319714271
ISBN-10: 3319714279
Pagini: 126
Ilustrații: VII, 128 p. 26 illus., 7 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.2 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3319714279
Pagini: 126
Ilustrații: VII, 128 p. 26 illus., 7 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.2 kg
Ediția:1st ed. 2018
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics
Locul publicării:Cham, Switzerland
Cuprins
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).
Textul de pe ultima copertă
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 theapproach 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.
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 theapproach 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.
Caracteristici
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