COMPLEX STABLE MANIFOLDS OF HOLOMORPHIC DIFFEOMORPHISMS

For any holomorphic diffeomorphism f on C(n) with an f-invariant compact subset K and any f-invariant probability Borel measure mu on K, we give the complex versions of the Oseledec multiplicative ergodic theorem and the Pesin stable manifold theorem. If f is a finite composition of complex Henon mappings of C2, K, J+ and J- are f-invariant sets defined in the introduction, and mu is the equilibrium measure introduced by Bedford, Smillie and Sibony on K, it is proved that for mu a.e. p is-an-element-of K, the stable/unstable manifolds are immersed holomorphic copies of C, and they are contained in J+/J-.