Analytic Regularity of Solutions of Livsic's Cohomology Equation and Some Applications to Analytic Conjugacy of Hyperbolic Dynamical Systems

We study Livsic's problem of nding satisfying X = where is a given function and X is a given Anosov vector eld. We show that, if is a continuous solution and X; are analytic, then is analytic. We use the previous result to show that if two low-dimensional Anosov systems are topologically conjugate and the Lyapunov exponents at corresponding periodic points agree, the conjugacy is analytic. Analogous results hold for diieomorphisms.