The Julia sets of quadratic Cremer polynomials

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• 作者：Alexander Blokh and Lex Oversteegen
• 关键词：Complex dynamics ; Julia set ; Cremer fixed point
• 刊名：Topology and its Applications
• 出版年：2006
• 出版时间：1 September 2006
• 年：2006
• 卷：153
• 期：15
• 页码：3038-3050
• 全文大小：192 K

文摘

We study the topology of the Julia set of a quadratic Cremer polynomial P. Our main tool is the following topological result. Let be a homeomorphism of a plane domain U and let MTK1-1&_mathId=mml2&_user=10&_cdi=5677&_rdoc=30&_handle=V-WA-A-W-BU-MsSAYWW-UUW-U-AAZCWVVAVD-AAZWYWVEVD-VWVBYUZZ-BU-U&_acct=C000050221&_version=1&_userid=10&md5=7098672b3f7c918df348d3550f307705"" title=""Click to view the MathML source"">TU be a non-degenerate invariant non-separating continuum. If T contains a topologically repelling fixed point x with an invariant external ray landing at x, then T contains a non-repelling fixed point. Given P, two angles θ,γ are K-equivalent if for some angles x₀