三角形映射的几何与代数
Geometry and Algebra of the Deltoid Map
摘要：
三角形曲线的几何形状产生$\mathbb{C}^2$的自映射，其在坐标中由$f(x,y) = (y^2 - 2x, x^2 - 2y)$表示。这是将切比雪夫多项式推广到多个变量的映射族中的一个。我们用这个例子来说明复杂动力学中的两个重要对象：朱利亚集和迭代单值群。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
