Rahul Sharma (Editor)

Complex dynamics

Updated on
Edit
Like
Comment
Share on FacebookTweet on TwitterShare on LinkedInShare on Reddit

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.

Contents

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
  • Yoccoz puzzles

    • 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.

    • References

    Complex dynamics Wikipedia
    (Text) CC BY-SA