Difference between revisions of "Complex dynamics"

Revision as of 16:18, 12 September 2015

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

• General
  • Montel's theorem
  • Poincaré metric
  • Schwarz lemma
  • Riemann mapping theorem
  • Carathéodory's theorem (conformal mapping)
  • Böttcher's equation
• Combinatorial <ref>Template:Citation</ref>
  • Hubbard trees
  • The Spider algorithm
  • Tuning
  • Laminations
  • Devil's Staircase algorithm
  • Orbit portraits

Parts

• Holomorphic dynamics ( dynamics of holomorphic functions )<ref>Surveys in Dynamical systems available on-line at Dynamical Systems Homepage of Institute for Mathematical Sciences SUNY at Stony Brook</ref>
  • 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

External links

• [Complex dynamics] @ Wikipedia