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
Poincaré metric
Schwarz lemma
Riemann mapping theorem
Carathéodory'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