Biaccessibility in Quadratic Julia Sets I: the Locally-connected Case
نویسنده
چکیده
Let f : z 7→ z + c be a quadratic polynomial whose Julia set J is locallyconnected. We prove that the Brolin measure of the set of biaccessible points in J is zero except when f(z) = z − 2 is the Chebyshev quadratic polynomial for which the corresponding measure is one. §
منابع مشابه
Biaccessibility in Quadratic Julia Sets
This paper consists of two nearly independent parts, both of which discuss the common theme of biaccessible points in the Julia set J of a quadratic polynomial f : z 7→ z + c. In Part I, we assume that J is locally-connected. We prove that the Brolin measure of the set of biaccessible points (through the basin of attraction of infinity) in J is zero except when f(z) = z−2 is the Chebyshev map f...
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