List questions from complex-dynamics

Published on 23 Mar 2023 - 23:05

189

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Is the interior of the mandelbrot set connected?

Published on 06 Apr 2023 - 9:27

107

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For a complex number on the unit circle with irrational argument z, does $z^{N!}$ ever converge?

Published on 15 Apr 2023 - 19:39

51

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Dynamics of the map $z \mapsto z^2$

Published on 15 Apr 2023 - 21:37

66

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Maclaurin series for $ f(f(z)) = \exp(z) - \exp(-z) + \exp(-z/2) - \exp(-z/5)+ \exp(-z/6) - \exp(-z/9)$

Published on 19 Apr 2023 - 22:38

79

Views

Inequality involving the distance to the nearest integer

Published on 25 Mar 2026 - 20:17

32

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Necessary condition for "finite-type" maps onto compact hyperbolic Riemann surfaces

Published on 09 May 2023 - 10:33

68

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Rational map satisfies Lipschitz condition.

Published on 09 May 2023 - 19:23

56

Views

Fatou and Julia sets under the conjugation.

Published on 10 May 2023 - 22:01

58

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Generalisation of Fatou-Julia theorem

Published on 24 Feb 2026 - 8:18

91

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Iterating $\tanh(A x)$ and $\lim_{x \to +\infty} \tanh^{[r]}(A x) = C_r$?

Published on 24 May 2023 - 23:19

41

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Reference/translation request: Doaudy and Hubbard

Published on 25 Mar 2026 - 12:31

100

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Non-zero critical value of a complex polynomial

Published on 04 Jul 2023 - 14:30

46

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How to prove that this polynomial inequality region is connected?

Published on 05 Jul 2023 - 4:07

77

Views

Critical points of rational mappings of annuli Fatou Component

Published on 24 Feb 2026 - 8:20

List Question

Oscillations in Newton's fractal

Is the interior of the mandelbrot set connected?

For a complex number on the unit circle with irrational argument z, does $z^{N!}$ ever converge?

Dynamics of the map $z \mapsto z^2$

Maclaurin series for $ f(f(z)) = \exp(z) - \exp(-z) + \exp(-z/2) - \exp(-z/5)+ \exp(-z/6) - \exp(-z/9)$

Inequality involving the distance to the nearest integer

Necessary condition for "finite-type" maps onto compact hyperbolic Riemann surfaces

Rational map satisfies Lipschitz condition.

Fatou and Julia sets under the conjugation.

Generalisation of Fatou-Julia theorem

Iterating $\tanh(A x)$ and $\lim_{x \to +\infty} \tanh^{[r]}(A x) = C_r$?

Reference/translation request: Doaudy and Hubbard

Non-zero critical value of a complex polynomial

How to prove that this polynomial inequality region is connected?

Critical points of rational mappings of annuli Fatou Component

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