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Tuesday, April 3, 2012

Dynamics in One Complex Variable






Intro du tory Le tures
(Partially revised version of 9-5-91)
John Milnor
Institute for Mathemati al S ien es, SUNY, Stony Bro ok NY
Table of Contents.
Prefa e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chronologi al Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Riemann Surfa es.
1. Simply Conne ted Surfa es . . . . . . . . . . . . . . . . . . . . (9 pages)
2. The Universal Covering, Montel’s Theorem . . . . . . . . . . . . . . . (5)
The Julia Set.
3. Fatou and Julia: Dynami s on the Riemann Sphere . . . . . . . . . . . (9)
4. Dynami s on Other Riemann Surfa es . . . . . . . . . . . . . . . . . (6)
5. Smo oth Julia Sets . . . . . . . . . . . . . . . . . . . . . . . . . . (4)
Lo al Fixed Point Theory.
6. Attra ting and Rep elling Fixed Points . . . . . . . . . . . . . . . . . (7)
7. Parab oli Fixed Points: the Leau-Fatou Flower . . . . . . . . . . . . . (8)
8. Cremer Points and Siegel Disks . . . . . . . . . . . . . . . . . . . . (11)
Global Fixed Point Theory.
9. The Holomorphi Fixed Point Formula . . . . . . . . . . . . . . . . . (3)
10. Most Perio di Orbits Rep el . . . . . . . . . . . . . . . . . . . . . . (3)
11. Rep elling Cy les are Dense in J . . . . . . . . . . . . . . . . . . . (5)
Stru ture of the Fatou Set.
12. Herman Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)
13. The Sullivan Classi ation of Fatou Comp onents . . . . . . . . . . . . (4)
14. Sub-hyp erb oli and hyp erb oli Maps . . . . . . . . . . . . . . . . . . (7)
Carath eo dory Theory.
15. Prime Ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)
16. Lo al Conne tivity . . . . . . . . . . . . . . . . . . . . . . . . . (4)
Polynomial Maps.
17. The Filled Julia Set K . . . . . . . . . . . . . . . . . . . . . . . (4)
18. External Rays and Perio di Points . . . . . . . . . . . . . . . . . . . (8)
App endix A. Theorems from Classi al Analysis . . . . . . . . . . . . . . . . (4)
App endix B. Length-Area-Mo dulus Inequalities . . . . . . . . . . . . . . . . (6)
App endix C. Continued Fra tions . . . . . . . . . . . . . . . . . . . . . . (5)
App endix D. Remarks on Two Complex Variables . . . . . . . . . . . . . . . (2)
App endix E. Bran hed Coverings and Orbifolds . . . . . . . . . . . . . . . . (4)
App endix F. Parameter Spa e . . . . . . . . . . . . . . . . . . . . . . . (3)
App endix G. Remarks on Computer Graphi s . . . . . . . . . . . . . . . . (2)
Referen es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)


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