R. de la Llave
Analytic regularity of solutions of Livsic's
cohomology equation and some applications to
analytic conjugacy of hyperbolic dynamical systems
(48K, LaTeX)
ABSTRACT. We study Livsic's problem of finding $\phi$
satisfying $X\phi=\eta$ where $\eta$ is a
given function and $X$ is a given Anosov
vector field.
We show that, if $\phi$ is a continuous solution
and $X,\eta$ are analytic, then $\phi$ 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 diffeomorphisms.