Linear cocycles over hyperbolic systems and their periodic data

CDSNS Colloquium
Monday, March 12, 2012 - 11:00am
1 hour (actually 50 minutes)
Skiles 006
Univ. of Southern Alabama
A linear cocycle over a diffeomorphism f of a manifold M is an automorphism of a vector bundle over M that projects to f. An important example is given by the differential Df or its restriction to an invariant sub-bundle. We consider a Holder continuous linear cocycle over a hyperbolic system and explore what conclusions can be made based on its properties at the periodic points of f. In particular, we obtain criteria for a cocycle to be isometric or conformal and discuss applications and further developments.