The Dimensions Of C~1 Average Conformal Hyperbolic Invariant Sets

This article investigates the dimensions of an C1 average conformal hyperbolic invariant set.Namely,let f:M ? M be a C1 diffeomorphism on a compact Reiman-nian manifold M,which admits a locally maximum hyperbolic invariant?((?)M).If? is average conformal,then the Hausdorff dimension of ? is the sum of the Haus-dorff dimensions of the stable and unstable foliations.This result is also true for box dimension of the average conformal hyperbolic invariant.