Poisson structures in the Banach setting: comparison of different approaches

Abstract

In this paper we examine various approaches to the notion of Poisson manifold in the context of Banach manifolds. Existing definitions are presented and differences between them are explored and illustrated with examples.

21 pages

References in corpus (14)

• Banach Lie-Poisson spaces and reduction
• Poisson brackets in Hydrodynamics
• Classical W-algebras for gl_N and associated integrable Hamiltonian hierarchies
• Double Poisson vertex algebras and non-commutative Hamiltonian equations
• Almost Lie structures on an anchored Banach bundle
• Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal
• Hierarchy of Hamilton equations on Banach Lie-Poisson spaces related to restricted Grassmannian
• Queer Poisson brackets
• A new scheme of integrability for (bi)Hamiltonian PDE
• Banach Poisson-Lie groups and Bruhat-Poisson structure of the restricted Grassmannian
• Convenient Partial Poisson Manifolds
• Geometry of quantum dynamics in infinite dimension
• Geometry of Integrable Systems Related to the Restricted Grassmannian
• Banach Poisson-Lie group structure on $U(\mathcal{H})$