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The solar Julia sets of basic quadratic Cremer polynomials. (English) Zbl 1184.37041

Summary: In general, little is known about the exact topological structure of Julia sets containing a Cremer point. In this paper we show that there exist quadratic Cremer Julia sets of positive area such that for a full Lebesgue measure set of angles the impressions are degenerate, the Julia set is connected im kleinen at the landing points of these rays, and these points are contained in no other impression.

MSC:

37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
37F10 Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
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References:

[1] Milnor, Dynamics in One Complex Variable (2000) · doi:10.1007/978-3-663-08092-3
[2] Munkres, Topology (2000)
[3] McMullen, Complex Dynamics and Renormalization (1994) · Zbl 0822.30002
[4] DOI: 10.1007/BF01231694 · Zbl 0781.30023 · doi:10.1007/BF01231694
[5] DOI: 10.2307/2159146 · Zbl 0773.30005 · doi:10.2307/2159146
[6] DOI: 10.1090/S0002-9947-99-02346-6 · Zbl 0946.30015 · doi:10.1090/S0002-9947-99-02346-6
[7] Lyubich, J. Differential Geom. 47 pp 17– (1997)
[8] Douady, Publ. Math. d’Orsay 84–02 (1984)
[9] DOI: 10.1016/S0001-8708(03)00144-0 · Zbl 1054.37025 · doi:10.1016/S0001-8708(03)00144-0
[10] Childers, Fields Inst. Commun. 53 pp 75– (2008)
[11] DOI: 10.1017/S0143385700000754 · Zbl 0966.37015 · doi:10.1017/S0143385700000754
[12] DOI: 10.1016/j.topol.2004.04.013 · Zbl 1127.37038 · doi:10.1016/j.topol.2004.04.013
[13] DOI: 10.1090/S0002-9939-96-03736-7 · Zbl 0866.54014 · doi:10.1090/S0002-9939-96-03736-7
[14] DOI: 10.1017/S0305004100072236 · Zbl 0823.58012 · doi:10.1017/S0305004100072236
[15] DOI: 10.1016/j.topol.2006.02.001 · Zbl 1099.37034 · doi:10.1016/j.topol.2006.02.001
[16] DOI: 10.1017/S0143385700001024 · Zbl 0970.37037 · doi:10.1017/S0143385700001024
[17] Yoccoz, Astérisque 231 (1995)
[18] Sullivan, Conformal Dynamical Systems pp 725– (1983) · Zbl 0524.58024
[19] DOI: 10.1017/S0143385798108301 · Zbl 0923.58039 · doi:10.1017/S0143385798108301
[20] DOI: 10.1090/S0002-9939-99-05111-4 · Zbl 0942.37036 · doi:10.1090/S0002-9939-99-05111-4
[21] Pommerenke, Boundary Behavior of Conformal Maps (1992) · doi:10.1007/978-3-662-02770-7
[22] DOI: 10.1007/BF02392621 · Zbl 0884.30020 · doi:10.1007/BF02392621
[23] DOI: 10.1007/BF02392745 · Zbl 0914.58027 · doi:10.1007/BF02392745
[24] Perez-Marco, Publ. Math. d’Orsay 94–48 (1994)
[25] DOI: 10.1007/BF02392901 · Zbl 0930.37022 · doi:10.1007/BF02392901
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