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Algebraic geometry --- Abelian varieties --- Abelse varieteiten --- Hamiltonian systems --- Hamiltonsystemen --- Systèmes hamiltoniens --- Varieties Abelian --- Variétés abéliennes --- Abelian varieties. --- Hamiltonian systems. --- Differentiable dynamical systems --- Dynamique différentiable --- Differentiable dynamical systems. --- Dynamique différentiable --- Systèmes hamiltoniens --- Equations differentielles sur une variete --- Geometrie algebrique --- Varietes abeliennes

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Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.

Geometry, Differential. --- Geometry. --- Hamiltonian systems. --- Poisson algebras. --- Poisson manifolds. --- Symplectic geometry. --- Poisson manifolds --- Poisson algebras --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Applied Mathematics --- Lie algebras. --- Differential geometry --- Algebras, Lie --- Mathematics. --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Mathematical analysis. --- Analysis (Mathematics). --- Differential geometry. --- Analysis. --- Differential Geometry. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Differentiable manifolds --- Global analysis (Mathematics). --- Global differential geometry. --- Topological Groups. --- Algebra. --- Mathematical analysis --- Groups, Topological --- Continuous groups --- Geometry, Differential --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Rings (Algebra) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- 517.1 Mathematical analysis --- Algebraic rings --- Ring theory --- Algebraic fields

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Lie algebras --- Differential equations --- Geometry, Algebraic --- Painlevé equations