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Activities

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Colloquium
Beginning2019-05-20 16:00:00
Ending2019-05-20 17:00:00
Event titleColloquium-From Cantor to Semi-hyperbolic Parameters along External Rays
Speaker陳怡全 研究員 (中央研究院)
PlaceLecture Room B, 4th Floor, The 3rd General Building
DescriptionClick here to read
Attached file File download Adobe PDF
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NoteAbstract
For the quadratic family f_c (z) = z^2+c with c in the exterior of the Mandelbrot set, it is well-known that every point in the Julia set moves holomorphically when c varies. Let \hat{c} be a semi-hyperbolic parameter in the boundary of the Mandelbrot set. In this talk, I shall show that for each z = z(c) in the Julia set, the derivative dz(c)/dc is uniformly O(1/\sqrt{|c-\hat{c}|}) when c belongs to a parameter ray that lands on \hat{c}. I shall also discuss the degeneration of the dynamics along the parameter ray.
Last Update Time2019-05-13 09:16:47
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