Poisson Structures and Their Normal Forms /
Dufour, Jean-Paul.
Poisson Structures and Their Normal Forms / by Jean-Paul Dufour, Nguyen Tien Zung ; edited by H. Bass, J. Oesterlé, A. Weinstein. - xv, 321 páginas recurso en línea. - Progress in Mathematics ; 242 .
Springer eBooks
Generalities on Poisson Structures -- Poisson Cohomology -- Levi Decomposition -- Linearization of Poisson Structures -- Multiplicative and Quadratic Poisson Structures -- Nambu Structures and Singular Foliations -- Lie Groupoids -- Lie Algebroids.
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.
9783764373351
10.1007/b137493 doi
QA252.3
Poisson Structures and Their Normal Forms / by Jean-Paul Dufour, Nguyen Tien Zung ; edited by H. Bass, J. Oesterlé, A. Weinstein. - xv, 321 páginas recurso en línea. - Progress in Mathematics ; 242 .
Springer eBooks
Generalities on Poisson Structures -- Poisson Cohomology -- Levi Decomposition -- Linearization of Poisson Structures -- Multiplicative and Quadratic Poisson Structures -- Nambu Structures and Singular Foliations -- Lie Groupoids -- Lie Algebroids.
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.
9783764373351
10.1007/b137493 doi
QA252.3