 96190 R. de la Llave
 Analytic regularity of solutions of Livsic's
cohomology equation and some applications to
analytic conjugacy of hyperbolic dynamical systems
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May 14, 96

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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
lowdimensional Anosov systems are topologically
conjugate and the Lyapunov exponents at
corresponding periodic points agree, the
conjugacy is analytic.
Analogous results hold for diffeomorphisms.
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96190.tex