Fatou directions along the Julia set for endomorphisms of

Abstract: We study the dynamics on the Julia set for holomorphic endomorphisms of . The Julia set is the support of the so-called Green current T, so it admits a natural filtration , where for we put . We show that for a generic point of there are at least “Fatou directions” in the tangent space. We also give estimates for the rate of expansion in directions transverse to the Fatou directions. [Copyright &y& Elsevier]