演講公告

演講主題：Family Of Julia Sets As Orbits Of Differential Equations
主講人：陳怡全教授（中央研究院數學所）
演講日期：2011年3月8日(星期二) 下午2:00 –3:00
演講地點：(光復校區) 科學一館223室
茶會時間：當天下午1:30 (科學一館205室)
摘要內容：
The Julia set of the quadratic map f_u(z)=u z(1-z) for u not belonging to the Mandelbrot set is hyperbolic. It follows that a continuous curve in the exterior of the Mandelbrot set induces a continuous family of Julia sets. We shall 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 u=infinity. We conduct numerical approximations to the Julia sets when parameter u is located at the Misiurewicz points with external angle 1/2, 1/6, or 5/12. When u 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.
相關檔案：演講1000308.doc

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