Family of Julia Sets as Orbits of Differential Equations
陳怡全 教授中央研究院數學所 下午 3:00–4:00 鴻經館 107 室The Julia sets of the quadratic map $f_\mu(z)=\mu z(1-z)$ for $\mu$ not belonging to the Mandelbrot set form a continuous family as $\mu$ varies. We show that this family can be obtained explicitly by solving a system of infinitely coupled differential equations. We also present numerical approximations to the Julia sets integrated from the anti-integrable limit $\mu=\infty$.