Family of Invariant Cantor Sets as Orbits of Differential Equations: II. Julia Sets
报告题目： Family of Invariant Cantor Sets as Orbits of Differential Equations: II. Julia Sets
报告人：陈怡全教授（台湾中央研究院数学研究所）
报告时间：2013年6月18日（星期二）下午4：15
报告地点：数学楼二楼学术报告厅
Abstract: The Julia set of the quadratic map $f_mu(z)=mu z(1-z)$ for $mu$ not belonging to the Mandelbrot set is hyperbolic, thus varies continuously. It follows that a continuous curve in the exterior of the Mandelbrot set induces a continuous family of Julia sets. The focus of this presentation is to show that this family can be obtained explicitly by solving the initial value problem of a system of infinitely coupled differential equations. A key point is that the required initial values can be obtained from the anti-integrable limit $muto infty$. We conduct numerical approximations to the Julia sets when parameter $mu$ is located at the Misiurewicz points with external angle $1/2$, $1/6$, or $5/12$. When $mu$ is at the Misiurewicz point of angle $1/128$, a $98$-period orbit of prescribed itinerary obtained by this method is presented, without having to find a root of a $2^{98}$-degree polynomial.
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