论文标题
有界的基因座和婴儿mandelbrot设置了一些广义的麦克穆伦地图
The Boundedness Locus and baby Mandelbrot sets for some generalized McMullen maps
论文作者
论文摘要
在本文中，我们研究了形式的$ r_ {n，a，c}（z）= z^n + \ dfrac {a} {z^n} + c，$，$ n $固定和至少$ 3 $的合理功能，并保持$ a $ a $或$ c $，而其他则固定。我们在某些$ a $的范围内找到了$ c $ - 参数飞机中设置的曼德布罗特的同构副本，以及一些$ c $ ranges的$ a $平面。 我们使用Douady和Hubbard首先引入的技术，这些技术适用于Robert Devaney的亚家族$ r_ {n，a，0} $。这些技术涉及第二学位的多项式图。
In this paper we study rational functions of the form $ R_{n,a,c}(z) = z^n + \dfrac{a}{z^n} + c, $ with $n$ fixed and at least $3$, and hold either $a$ or $c$ fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the $c$-parameter plane for certain ranges of $a$, as well as in the $a$-plane for some $c$-ranges. We use techniques first introduced by Douady and Hubbard, that were applied for the subfamily $R_{n,a,0}$ by Robert Devaney. These techniques involve polynomial-like maps of degree two.
