Cubic polynomials with a parabolic point
Cubic polynomials with a parabolic point
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DOI：
10.1017/s0143385709000820
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发表时间：
2007-12
影响因子：
0.9
通讯作者：
P. Roesch
中科院分区：
文献类型：
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作者：
P. Roesch
摘要考虑三次多项式的一个简单抛物不动点的乘子为1。对于这些映射，我们证明了抛物点的直接吸引盆的边界是一条Jordan曲线（除了多项式z+z3，它由两条Jordan曲线组成）。此外，我们给出了动力学的描述，并在一定的假设下得到了Julia集的局部连通性。
Abstract We consider cubic polynomials with a simple parabolic fixed point of multiplier 1. For those maps, we prove that the boundary of the immediate basin of attraction of the parabolic point is a Jordan curve (except for the polynomial z+z3 where it consists in two Jordan curves). Moreover, we give a description of the dynamics and obtain the local connectivity of the Julia set under some assumptions.