Almost Lie structures on an anchored Banach bundle

Abstract

Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolutionary problem of the "Hilbert snake"

References in corpus (4)

• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics
• Differential calculus on a Lie algebroid and Poisson manifolds
• Integrability of weak distributions on Banach manifolds
• Banach Lie algebroids

Cited by in corpus (15)

• Queer Poisson brackets
• Poisson structures on almost complex Lie algebroids
• Banach Poisson-Lie groups and Bruhat-Poisson structure of the restricted Grassmannian
• Convenient Partial Poisson Manifolds
• Algebroids associated to the groupoid of partially invertible elements of a $W^{\ast }$-algebra
• Fibre-wise linear Poisson structures related to W*-algebras
• Integrability of weak distributions on Banach manifolds
• Integrability on Direct Limit Banach manifolds
• Poisson geometrical aspects of the Tomita-Takesaki modular theory
• Banach Lie groupoid of partial isometries over restricted Grassmannian
• Banach Poisson-Lie group structure on $U(\mathcal{H})$
• Poisson structures in the Banach setting: comparison of different approaches
• Banach-Lie groupoids and generalized inversion
• On almost complex Lie algebroids
• Banach Poisson-Lie groups, Lax equations and the AKS theorem in infinite dimensions