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.

(TO DO: expand, organize, cross-reference, illustrate.)

Techniques

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

Parts

• Holomorphic dynamics ( dynamics of holomorphic functions )
  • 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

• Analytic function
• Chaos theory
• Complex number
• Complex analytic dynamics
• Complex analysis
• Complex quadratic polynomial
• Differentiable dynamics
• Dynamical system
• Fatou set
• Holomorphic function
• Infinite compositions of analytic functions
• Iterated function
• Julia set
• Mandelbrot set
• Mathematics
• Milnor, John

External links

• Complex dynamics @ Wikipedia