On some limits in the theory of Julia sets

Abstract: We will speak about polynomial Julia sets in the complex plane, even though most subjects can be investigated also in higher dimensions. We consider some approximation problems. One of them is approximation of some regular sets by polynomial Julia sets. It can be seen that a good tool for this approximation is Klimek’s metric defined with use of Green's functions of complex sets, which is more appropriate than the classical Hausdorff metric. Another problem concerns creating computer pictures of some composite Julia sets. Finally, we deal with some sequences defined with use of (compositions of) Chebyshev polynomials and obtain their uniform limit.

complex variablesdynamical systems

Audience: researchers in the topic

CAvid: Complex Analysis video seminar

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