Smooth conjugacy and S-R-B measures for uniformly and non-uniformly hyperbolic systems (Q1207999)

The paper is devoted to a proof of the following theorem and its generalizations: Let \(f\), \(g\) be two \(C^ k\), \(k = 2,3,\dots,\infty\), \(\omega\) Anosov diffeomorphisms of a compact two-dimensional manifold \(M\) (respectively \(\sigma_ t\), \(\phi_ t\) two Anosov flows of a three dimensional manifold) and \(h\) a homeomorphism of \(M\) satisfying: \(h \circ f = g \circ h\) (respectively \(h \circ \sigma_ t = \phi_ t \circ h\)). If the Lyapunov exponents at corresponding periodic orbits are the same, then \(h \in C^{k-\varepsilon}\).