EUDML | On regular polynomial endomorphisms of ℂ2 without bounded critical orbitswithout bounded critical orbits

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Displaying similar documents to “On regular polynomial endomorphisms of ℂ2 without bounded critical orbitswithout bounded critical orbits”

Structurally stable perturbations of polynomials in the Riemann sphere

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For a class of quadratic polynomial endomorphisms $f : ℂ^{2} \to ℂ^{2}$ close to the standard torus map $(x, y) \to (x^{2}, y^{2})$ , 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).

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We survey known results about polynomial mating, and pose some open problems.

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Milnor, John (2004)

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Some open problems in higher dimensional complex analysis and complex dynamics.

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We present a collection of problems in complex analysis and complex dynamics in several variables.