论文标题
三角肌地图的几何形状和代数
Geometry and Algebra of the Deltoid Map
论文作者
论文摘要
三角形曲线的几何形状产生了$ \ mathbb {c}^2 $的自图，该自图在坐标中以$ f（x，y）=（y^2-2-2-2-2x，x^2-2y）$表示。这是一个地图家族中的一个，将Chebyshev多项式概括为几个变量。我们使用此示例来说明复杂动力学中的两个重要对象：朱莉娅集合和迭代的单片组。
The geometry of the deltoid curve gives rise to a self-map of $\mathbb{C}^2$ that is expressed in coordinates by $f(x,y) = (y^2 - 2x, x^2 - 2y)$. This is one in a family of maps that generalize Chebyshev polynomials to several variables. We use this example to illustrate two important objects in complex dynamics: the Julia set and the iterated monodromy group.
