Analytic regularity of solutions of Livsic's
cohomology equation and some applications to
analytic conjugacy of hyperbolic dynamical systems
1997 ◽
Vol 17
(3)
◽
pp. 649-662
◽
Keyword(s):
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.
1998 ◽
Vol 18
(2)
◽
pp. 471-486
◽
2013 ◽
Vol 35
(3)
◽
pp. 968-993
◽
2015 ◽
Vol 22
(1)
◽
pp. 140-146
◽
2006 ◽
Vol 16
(09)
◽
pp. 2729-2736
◽