The Mandelbrot and Julia sets Anatomy
Contents

• Introduction
  "M-set anatomy" remake
• Quick tour   Robert L. Devaney
  • Rotation numbers and internal angles of the M-bulbs
  • The primary M-bulbs counting
  • The secondary and The third level M-bulbs
• Iterations of quadratic maps
  • Iterations of real maps
  • Bifurcation diagram for quadratic maps
  • Iterations on complex plane. The Mandelbrot, Julia and Fatou sets
  • Iterations of inverse maps
• The Julia set
  • The Julia set symmetry
  • Critical points and Fatou theorem
  • The Fundamental Dichotomy for J-set
• Attractors, repellers...
  • The fixed points and periodic orbits
  • Local dynamics at a fixed point   Spiral structures in the Julia set
  • Attracting fixed point and period-2 orbit
  • Tangent bifurcations
  • Period doubling and period tripling bifurcations
  • Parabollic fixed points and Siegel disk
• Renormalization theory
  • Windows of periodicity scaling. The "linear" approximation.
  • The Julia set and The Mandelbrot set renormalization
  • Polynomial-like maps. Renormalization.   Nuria Fagella
  • Rabbit's show. Shaggy midgets.
• Periodic and preperiodic points
  • Periodic and preperiodic points in the M-set
  • Misiurewicz points and the M-set self-similarity   Douglas C. Ravenel
  • The M and J-sets similarity. Lei's theorem   Douglas C. Ravenel
  • Embedded Julia midgets
• Shrubs ordering   Miguel Romera
• Illustrations
  • The Julia set animation
  • 600x600 Mandelbrot set with the Boundary Tracing and
    Distance Estimator algorithms

Chaotic maps