Damian Brunold

John Milnor: Dynamics in One Complex Variable


Introductory Lectures, Second Edition


  1. (Riemann Surfaces) Simply Connected Surfaces
  2. Univeral Coverings and the Poincaré Metric
  3. Normal Families: Montel's Theorem
  4. (Iterated Holomorphic Maps) Fatou and Julia: Dynamics on the Riemann Sphere
  5. Dynamics on Hyperbolic Surfaces
  6. Dynamics on Euclidian Surfaces
  7. Smooth Julia Sets
  8. (Local Fixed Point Theory) Geometrically Attracting and Repelling Fixed Points
  9. Böttcher's Theorem and Polynomial Dynamics
  10. Parabolic Fixed Points: the Leau-Fatou Flower
  11. Cremer Points and Siegel Disks
  12. (Periodic Points: Global Theory) The Holomorphic Fixed Point Formula for Rational Maps
  13. Most Periodic Orbits Repel
  14. Repelling Cycles are Dense in J
  15. (Structure of the Fatou Set) Herman Rings
  16. The Sullivan Classification of Fatou Components
  17. (Using the Fatou Set to study the Julia Set) Prime Ends and Local Connectivity
  18. Polynomial Dynamics: External Rays
  19. Hyperbolic and Subhyperbolic Maps