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Geometry, Differential --- Global analysis (Mathematics) --- Géométrie différentielle --- Analyse globale (Mathématiques)

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Global analysis (Mathematics) --- Ideals (Algebra) --- Numerical functions --- Analyse globale (Mathématiques) --- Idéaux (Algèbre)

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Global analysis (Mathematics) --- Analyse globale (mathématiques) --- Differentiable dynamical systems. --- Systèmes dynamiques --- Groupes topologiques

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The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: sympletic topology. Surprising rigidity phenomena demonstrate that the nature of sympletic mappings is very different from that of volume preserving mappings. This raises new questions, many of them still unanswered. On the other hand, analysis of an old variational principle in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities. These invariants are the main theme of this book, which includes such topics as basic sympletic geometry, sympletic capacities and rigidity, periodic orbits for Hamiltonian systems and the action principle, a bi-invariant metric on the sympletic diffeomorphism group and its geometry, sympletic fixed point theory, the Arnold conjectures and first order elliptic systems, and finally a survey on Floer homology and sympletic homology. The exposition is self-contained and addressed to researchers and students from the graduate level onwards.

Mathematics --- Global analysis (Mathematics) --- Global differential geometry --- Mathématiques --- Analyse globale (Mathématiques) --- Géométrie différentielle globale

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Differential geometry. Global analysis --- Geometry --- Congresses. --- Global analysis (Mathematics) --- Analyse globale (mathématiques) --- Géometrie différentielle --- Analyse globale (mathématiques) --- Géometrie différentielle