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Geometrical Themes Inspired by the N-body Problem (Paperback, 1st ed. 2018)
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Geometrical Themes Inspired by the N-body Problem (Paperback, 1st ed. 2018)
Series: Lecture Notes in Mathematics, 2204
Expected to ship within 9 - 15 working days
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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topological detours, and providing historical references.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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