Abstract
Some recent work in Fr´echet geometry is briefly reviewed. In particular
an earlier result on the structure of second tangent bundles in the finite dimensional
case was extended to infinite dimensional Banach manifolds and Fr´echet manifolds that
could be represented as projective limits of Banach manifolds. This led to further results
concerning the characterization of second tangent bundles and differential equations in
the more general Fr´echet structure needed for applications. A summary is given of
recent results on hypercyclicity of operators on Fr´echet spaces.
an earlier result on the structure of second tangent bundles in the finite dimensional
case was extended to infinite dimensional Banach manifolds and Fr´echet manifolds that
could be represented as projective limits of Banach manifolds. This led to further results
concerning the characterization of second tangent bundles and differential equations in
the more general Fr´echet structure needed for applications. A summary is given of
recent results on hypercyclicity of operators on Fr´echet spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 6-21 |
| Journal | Balkan Journal of Geometry and Its Applications |
| Volume | 17 |
| Issue number | 2 |
| Publication status | Published - 2012 |
Keywords
- Banach manifold; Fr´echet manifold; projective limit; connection; second tangent bundle, frame bundle, differential equations, hypercyclicity