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E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA316.SPR. FCT 98435 (Browse shelf) | 1 | Available |
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QA9.SPR. FCT 98411 The hyperuniverse project and maximality | QA331.7.SPR. FCT 98412 Complex analysis and dynamical systems | QA612.SPR. FCT 98427 Singularities and foliations | QA316.SPR. FCT 98435 Geometrical themes inspired by the N-body problem | QA564.SPR. FCT 98438 Dynamical aspects of teichmüller theory | 86084 Otimização de resistências mecânicas do cimento com base nas suas características químicas e mineralógicas | 86085 Comparação de métodos para a caracterização quantitativa de copolímeros de Acrilonitrilo |
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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from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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.
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