PoissonGeometrie
PoissonGeometrie is a mathematical framework that integrates concepts from Poisson geometry and differential geometry to study geometric structures endowed with a Poisson bracket. Rooted in the work of Siméon Denis Poisson and further developed in the context of symplectic and Hamiltonian mechanics, Poisson geometry offers a generalized setting for analyzing dynamical systems, particularly those that do not possess a globally symplectic structure.
A Poisson manifold is a smooth manifold equipped with a Poisson bracket—a bilinear, antisymmetric operation on
PoissonGeometrie encompasses various topics, including the study of Poisson tensors, Lie algebroids, Casimir functions, and symplectic
Applications of PoissonGeometrie are widespread in mathematical physics, differential equations, and integrable systems. It also provides
Overall, PoissonGeometrie serves as a fundamental discipline in modern geometry, bridging algebraic and differential approaches to