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Non-landing parameter rays of the multicorns

机译:多角形的非着陆参数射线

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It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. We study the rational parameter rays of the multicorn , the connectedness locus of unicritical antiholomorphic polynomials of degree d, and give a complete description of their accumulation properties. One of the principal results is that the parameter rays accumulating on the boundaries of odd period (except period 1) hyperbolic components of the multicorns do not land, but accumulate on arcs of positive length consisting of parabolic parameters. We also show the existence of undecorated real-analytic arcs on the boundaries of the multicorns, which implies that the centers of hyperbolic components do not accumulate on the entire boundary of , and the Misiurewicz parameters are not dense on the boundary of .
机译:众所周知,Mandelbrot集的每个有理参数射线均落在单个参数上。我们研究了多角形的有理参数射线,d阶单临界反亚纯多项式的连通性轨迹,并对它们的累加特性进行了完整的描述。主要结果之一是,在奇数周期(周期1除外)的边界上累积的参数射线不会降落,而是在由抛物线参数组成的正长弧上聚集。我们还显示了在多角形的边界上存在未修饰的实分析弧,这表明双曲分量的中心未累积在的整个边界上,并且Misiurewicz参数在的边界上并不密集。

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