Smoothness of holonomies for codimension 1 hyperbolic dynamics

Abstract

Hyperbolic invariant sets {Lambda} of C1+{gamma} diffeomorphisms where either the stable or unstable leaves are 1-dimensional are considered in this paper. Under the assumption that the {Lambda} has local product structure, the authors prove that the holonomies between the 1-dimensional leaves are C1+{alpha} for some 0 < {alpha} < 1