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# 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[1]

General

Montel's theorem

PoincarÃ© metric

Schwarz lemma

Riemann mapping theorem

CarathÃ©odory's theorem (conformal mapping)

Combinatorial [2]

Hubbard trees

The Spider algorithm

Tuning

Laminations

Devil's Staircase algorithm

Orbit portraits

Parts

Holomorphic dynamics ( dynamics of holomorphic functions )[3]

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

Complex analysis

John Milnor

Complex quadratic polynomial

Fatou set

Julia set

Mandelbrot set

Chaos Theory

Infinite compositions of analytic functions

References

^ The Mandelbrot Set, Theme and Variations (London Mathematical Society Lecture Note Series) (No 274) by Tan Lei (Editor), Cambridge University Press, 2000

^ Flek, Ross; Keen L (July 13, 2009). "Boundaries of Bounded Fatou Components of Quadratic Maps" (in eng). RESEARCH ARTICLE. pp. 1{18. Retrieved 2009-09-07.

^ Surveys in Dynamical systems available on-line at Dynamical Systems Homepage of Institute for Mathematical Sciences SUNY at Stony Brook

Complex dynamics, Lennart Carleson, Theodore W. Gamelin, Springer, 1993, ISBN 9780387979427

Holomorphic dynamics, Shunsuke Morosawa, Cambridge University Press, 2000, ISBN 9780521662581

Iteration of rational functions: complex analytic dynamical systems, Alan F. Beardon, Springer, 2000, ISBN 9780387951515

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