Optimization of Lyapunov exponents of matrix cocycles
Jairo Bochi · Open Collections · 2015
I will discuss the problem of optimizing (i.e., maximizing or minimizing) the upper Lyapunov exponent of a matrix cocycle. The main result to be presented, joint with Michal Rams (Warsaw), says that if a 2x2 one-step cocycle has certain hyperbolicity properties (namely, there exist strictly invariant cones whose images do not overlap) then the Lyapunov-optimizing measures have zero entropy. The proof has two steps: first, a generalization of the Barabanov norm (similar to Man ̃ ́e lemma) and second, a study of geometrical constraints between the invariant directions.\r