Complex dynamics

Complex dynamics is the study of dynamical systems defined by iteration of functions on complex number spaces. Complex analytic dynamics is the study of the dynamics of specifically analytic functions.

Techniques

General
*Montel's theorem
*Poincaré metric
*Schwarz lemma
*Riemann mapping theorem
*Carathéodory's theorem
*Böttcher's equation
Combinatorial
* Hubbard trees
* Spider algorithm
* Tuning
*Laminations
*Devil's Staircase algorithm
*Orbit portraits
*Yoccoz puzzles
Parts
Holomorphic dynamics
* in one complex variable
* in several complex variables
Conformal dynamics unites holomorphic dynamics in one complex variable with differentiable dynamics in one real variable.

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