Displaying similar documents to “Complex dynamics, value distributions, and potential theory.”

Jordan tori and polynomial endomorphisms in 2

Manfred Denker, Stefan Heinemann (1998)

Fundamenta Mathematicae

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For a class of quadratic polynomial endomorphisms f : 2 2 close to the standard torus map ( x , y ) ( x 2 , y 2 ) , we show that the Julia set J(f) is homeomorphic to the torus. We identify J(f) as the closure ℛ of the set of repelling periodic points and as the Shilov boundary of the set K(f) of points with bounded forward orbit. Moreover, it turns out that (J(f),f) is a mixing repeller and supports a measure of maximal entropy for f which is uniquely determined as the harmonic measure for K(f).