Continuity properties of Lyapunov exponents for surface diffeomorphisms (Q2084781)

The paper deals with the discontinuity properties of the entropy and Lyapunov exponents of invariant measures \(\mu\) for smooth surface diffeomorphisms \(f\), as functions of \({(f,\mu)}.\) One of the main theorems is a new result on the existence of SRB measures with positive entropy. Namely, let \(f\) be a \({C^\infty}\) diffeomorphism of a compact surface without boundary. If there exist ergodic invariant probability measures \(\nu_k\), with entropy uniformly bounded away from zero, and such that the unstable dimension \(\delta^u(\nu_k)\to1,\) then \(f\) admits an ergodic SRB measure.