## Lyapunov exponents for small random perturbations of predominantly hyperbolic two dimensional volume-preserving diffeomorphisms, including the Standard Map

Alex Blumenthal

University of Maryland

November 19, 2018

An outstanding problem in smooth ergodic theory is the estimation from below of Lyapunov exponents for maps which exhibit hyperbolicity on a large but non- invariant subset of phase space. It is notoriously difficult to show that Lypaunov exponents actually reflect the predominant hyperbolicity in the system, due to cancellations caused by the“switching” of stable and unstable directions in those parts of phase space where hyperbolicity is violated.