LDR 03516     2200385   4500
010    _a9783319714271
011    _a0075-8434
090    _a16642
101    _aeng
102    _aCH
100    _a20140505              frey50       
200    _aGeometrical themes inspired by the N-body problem
       _fLuis Hernández-Lamoneda, Haydeé Herrera, Rafael Herrera, editors
210    _aCham
215    _a1 vol. (VII-125 p.)
225    _aLecture notes in mathematics
300    _aTextes issus de trois mini-cours donnés lors du 7e "Mini-meeting on differential geometry", tenu au Center for research in mathematics (CIMAT) de Guanajuato, Mexico, 17-19 février 2015
320    _aBibliogr. en fin de contributions
330    _aPublisher’s description: 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from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references.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.
410    _9132706
       _tLecture notes in mathematics
676    _a2010
686    _20
       _bDifferential geometry
       _xProceedings, conferences, collections, etc.
686    _20
       _bMechanics of particles and systems -- Dynamics of a system of particles, including celestial mechanics
       _xThree-body problems
686    _20
       _bDynamical systems and ergodic theory -- Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
       _xPeriodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
686    _20
       _bDifferential geometry -- Global differential geometry
       _xGeneral geometric structures on manifolds (almost complex, almost product structures, etc.)
686    _20
       _bDifferential geometry -- Symplectic geometry, contact geometry
       _xLagrangian submanifolds; Maslov index
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702    _4340
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856    _uhttps://zbmath.org/?q=an%3A06823408
856    _uhttps://mathscinet.ams.org/mathscinet-getitem?mr=3753576
856    _uhttps://link.springer.com/book/10.1007/978-3-319-71428-8
905    _aaw
906    _aaw
001     16642
995    _f12499-01
       _xachat Ebsco
       _k53-06 HER
       _eSalle R
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