- exterior of M-set = its complement
- M-set:
- boundary of M-set
- interior of M-set = hyperbolic components of M-set = critical point in dynamical plane is in periodic orbit

Mandelbrot set is a subset of complex (parameter ) plane :

The Mandelbrot set is a compact set it means that it is closed and bounded.

A closed set contains its own boundary = its complement is open.

(Absolute) complement of M-set in C-plane is its exterior.

Hyperbolic component is open set. It does not contain its boundary.

All Misiurewicz points belong to the boundary of the Mandelbrot set

Sets in

- basin of attraction of infinite attractor ( infinity ) = D
_{f}(infinity) - common boundary = (true) Julia set : J(f)
- basin of attraction of finite attractors ( point or cycle)= interior of filled Julia set

From The Mandelbrot, Julia and Fatou sets by Evgeny Demidov.

"Points on complex z plane (dynamical or variable space) which under iterations fc for fixed c go to an attractor (attracting fixed point, periodic orbit or infinity) form the

So C = F(f) + J(f) = K(f) + D

Autor: adammaj1-at-o2-dot--pl Adam Majewski

Feel free to e-mail me. (:-))

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