Weak Hyperbolicity on Periodic Orbits for Polynomials
نویسنده
چکیده
We prove that if the multipliers of the repelling periodic orbits of a complex polynomial grow at least like n 5+ε , for some ε > 0, then the Julia set of the polynomial is locally connected when it is connected. As a consequence for a polynomial the presence of a Cremer cycle implies the presence of a sequence of repelling periodic orbits with " small " multipliers. Somehow surprisingly the proof is based in measure theorical considerations.
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