List questions from complex-dynamics

Published on 15 Apr 2026 - 4:00

191

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Is the interior of the mandelbrot set connected?

Published on 14 Apr 2026 - 5:29

110

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

Published on 14 Apr 2026 - 12:21

54

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

Published on 14 Apr 2026 - 2:10

69

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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 16 Apr 2026 - 1:04

79

Views

Inequality involving the distance to the nearest integer

Published on 25 Mar 2026 - 20:17

35

Views

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

Published on 13 Apr 2026 - 19:44

71

Views

Rational map satisfies Lipschitz condition.

Published on 16 Apr 2026 - 12:30

59

Views

Fatou and Julia sets under the conjugation.

Published on 15 Apr 2026 - 17:57

61

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Generalisation of Fatou-Julia theorem

Published on 30 Apr 2026 - 20:00

94

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

Published on 13 Apr 2026 - 22:33

44

Views

Reference/translation request: Doaudy and Hubbard

Published on 11 May 2026 - 1:57

103

Views

Non-zero critical value of a complex polynomial

Published on 10 Apr 2026 - 16:46

49

Views

How to prove that this polynomial inequality region is connected?

Published on 14 Apr 2026 - 3:31

80

Views

Critical points of rational mappings of annuli Fatou Component

Published on 01 May 2026 - 18:52

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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