Complex dynamics
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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.
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[edit] Techniques[1]
- General
- Combinatorial [2]
- Hubbard trees
- The Spider algorithm
- Tuning
- Laminations
- Devil's Staircase algorithm
- Orbit portraits
[edit] 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.
[edit] See also
- Complex analysis
- John Milnor
- Complex quadratic polynomial
- Fatou set
- Julia set
- Mandelbrot set
- Chaos Theory
- Infinite compositions of analytic functions
[edit] 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. http://comet.lehman.cuny.edu/keenl/FlekKeenJDEA.pdf. 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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