View source for Complex dynamics

'''Complex dynamics''' is the study of [[dynamical system]]s defined by [[Iterated function|iteration]] of functions on [[complex number]] spaces. '''Complex analytic dynamics''' is the study of the dynamics of specifically [[analytic function]]s.

== Techniques ==

* General
** [[Montel's theorem]] 
** [[Poincaré metric]]
** [[Schwarz lemma]]
** [[Riemann mapping theorem]]
** [[Carathéodory's theorem (conformal mapping)]]
** [[Böttcher's equation]]
* [[Combinatorics|Combinatorial]]
** Hubbard trees
** The Spider algorithm
** Tuning
** [[Lamination (topology)|Laminations]]
** [[Cantor function|Devil's Staircase algorithm]]
** [[Orbit portrait]]s

== Parts ==

* '''Holomorphic dynamics''' ( dynamics of [[holomorphic function]]s )
** in one complex variable
** in several complex variables

* '''Conformal dynamics''' unites holomorphic dynamics in one complex variable with [[differentiable dynamics]] in one real variable.

== See also ==

* [[Analytic function]]
* [[Chaos theory]]
* [[Complex number]]
* [[Complex analytic dynamics]]
* [[Complex analysis]]
* [[Complex quadratic polynomial]]
* [[Differentiable dynamics]]
* [[Dynamical systems]]
* [[Fatou set]]
* [[Holomorphic function]]
* [[John H. Hubbard|Hubbard, John H.]]
* [[Infinite compositions of analytic functions]]
* [[Iterated function]]
* [[Julia set]]
* [[Mandelbrot set]]
* [[Mathematics]]
* [[John Milnor|Milnor, John]]

== External links ==

* [https://en.wikipedia.org/wiki/Complex_dynamics Complex dynamics] @ Wikipedia

[[Category:Mathematics]]