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Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical problems, and form a bridge from the "commutative world" to the "noncommutative world". The aim of this book is twofold: On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects, including singular foliations, Lie groupoids and Lie algebroids. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

Poisson manifolds. --- Lie algebras. --- Geometry, Differential. --- Symplectic geometry. --- Hamiltonian systems. --- Lagrange spaces. --- Spaces, Lagrange --- Geometry, Differential --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Differential geometry --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Differentiable manifolds --- Topological Groups. --- Topological Groups, Lie Groups. --- Groups, Topological --- Continuous groups --- Topological groups. --- Lie groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

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Poisson manifolds play a fundamental role in Hamiltonian dynamics, where they serve as phase spaces. They also arise naturally in other mathematical problems, and form a bridge from the "commutative world" to the "noncommutative world". The aim of this book is twofold: On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects, including singular foliations, Lie groupoids and Lie algebroids. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

Topological groups. Lie groups --- topologie (wiskunde)

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Géométrie symplectique. --- Feuilletages (mathématiques) --- Singularités (mathématiques) --- Systèmes hamiltoniens. --- Symplectic geometry --- Foliations (Mathematics) --- Singularities (Mathematics) --- Hamiltonian systems --- Géométrie symplectique. --- Feuilletages (mathématiques) --- Singularités (mathématiques) --- Systèmes hamiltoniens.