Induction for weak symplectic Banach manifolds
Copyright policy )Induction for weak symplectic Banach manifolds
This paper extends the symplectic induction procedure to the case of weak symplectic Banach manifolds. On weak symplectic manifolds not all smooth functions admit a Hamiltonian vector field. The authors first introduce the Poisson subalgebra of smooth functions that admit Hamiltonian vector fields. The symplectic induction procedure on weak symplectic manifolds is then presented. The theory is finally applied to several examples of Banach manifolds, namely, the Banach Lie group of \(k\)-diagonal operators. Explicit formulas are also obtained.
- University of Białystok Poland
- Polish Academy of Sciences Poland
- Institute of Mathematics Poland
- École Polytechnique Fédérale de Lausanne EPFL Switzerland
Infinite-dimensional manifolds, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Banach space, Symplectic manifolds (general theory), Hamiltonian vector field, Poisson manifolds; Poisson groupoids and algebroids, Applications of differential geometry to physics, symplectic manifold, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Banach Lie-Poisson space, Applications of functional analysis to differential and integral equations
Infinite-dimensional manifolds, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Banach space, Symplectic manifolds (general theory), Hamiltonian vector field, Poisson manifolds; Poisson groupoids and algebroids, Applications of differential geometry to physics, symplectic manifold, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds, Banach Lie-Poisson space, Applications of functional analysis to differential and integral equations
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!