On Closed Invariant Sets in Local Dynamics
نویسنده
چکیده
We investigate the dynamical behaviour of a holomorphic map f : U → C , where U is an open polynomially convex subset of C, on an f−invariant subset E of U. We also prove a Birkhoff type Theorem for holomorphic maps in several complex variables, i.e. given an injective holomorphic map f, defined in a neighborhood of U, with U star-shaped and f(U) a Runge domain, we prove the existence of a forward invariant, maximal, compact and connected subset of U which touches ∂U.
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