An isolated Lyapunov exponent

Abstract

We construct a continuous linear cocycle over an expanding base dynamics for which the Lyapunov exponents of all ergodic invariant probability measures are small, except for one measure whose Lyapunov exponents are away from zero. The support of this distinguished measure is not a periodic orbit. In particular, our example violates the periodic approximation property.

v.2: Revised according to the referee report. Final version, accepted for publication in Proc. Amer. Math. Soc