Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials
نویسندگان
چکیده
منابع مشابه
Rigidity and non local connectivity of Julia sets of some quadratic polynomials
For an infinitely renormalizable quadratic map fc : z 7→ z 2+c with the sequence of renormalization periods {nm} and the rotation numbers {tm = pm/qm}, we prove that if lim supn−1 m log |pm| > 0, then the Mandelbrot set is locally connected at c. We prove also that if lim sup |tm+1| 1/qm < 1 and qm → ∞, then the Julia set of fc is not locally connected provided c is the limit of corresponding c...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2009
ISSN: 0024-6115
DOI: 10.1112/plms/pdn055