4:00 pm Thursday, October 7, 2010

Boris Kalinin (University of South Alabama)

A linear cocycle over a dynamical system ƒ : *M* → *M* is an automorphism
of a vector bundle over *M* that projects to ƒ. An important example comes
from the differential *D*ƒ or its restriction to an invariant sub-bundle of *TM*.
For a trivial bundle with fiber *R*^{d}, a linear cocycle can be simply viewed as
a *GL(d,R)*-valued function on the manifold. We consider Hoelder continuous
linear cocycles over hyperbolic systems. In this case it is natural to look at the
behavior of a cocycle at the periodic orbits of the system, which we call the
periodic data. We discuss what conclusions can be made about the cocycle
based on its periodic data. In particular, we obtain criteria for a cocycle
to be isometric or conformal.