Holomorphic dynamical systems
Course - 2018-2019 (1st semester) - Beijing University and BICMR.
The first 12 lessons are for 4th year Maths. The last 4 lessons are for graduate-Phd students.
All classes will take place in Room 9, Quan Zhai, BICMR (see
link).
Time schedule
- 2018.09.04: Tuesday 15h00-18h00 - room 9 Qyan Zhai, BICMR
- 2018.09.11: Tuesday 15h00-18h00 - room 29 Qyan Zhai, BICMR
- From 2018.09.17 to 2018.11.18: Fridays 14h00-17h00 - room 9 Qyan Zhai, BICMR
- From 2018.11.19: Tuesdays 09h00-12h00 - room 9 Qyan Zhai, BICMR
Period and variations to the time schedule
- From 2018.09.04 to 2018.12.28
- National Holiday 2018.10.01-07 : no class
- The class of 2018.10.12 will not take place : it is moved to 2018.10.16 09h00-12h00 room 9 Qyan Zhai
- The class of 2018.11.02 is moved to 2018.11.06 09h00-12h00 room 9 Qyan Zhai
- The class of 2018.11.09 is moved to 2018.11.13 09h00-12h00 room 9 Qyan Zhai
Suggested references
- Milnor - Dynamics in one complex variable (3rd edition, 2006).
- Beardon - Iteration of rational functions (2000).
- Carleson, Gamelin - Complex dynamics (1993).
Personal handwritten notes of the classes
Be careful, there could be mistakes, and it could differ from the given classes.
- Class 01, 2018.09.04: 01 - Introduction. pdf
- Class 01, 2018.09.04: 02a - Holomorphic functions. pdf
- Class 02, 2018.09.11: 02b - Riemann surfaces and coverings. pdf
- Class 03, 2018.09.21: 02c - Poincaré metric. pdf
- Class 04, 2018.09.28: 03a - Local uniform convergence. pdf
- Class 04, 2018.09.28: 03b - Normal families. pdf
- Class 05, 2018.10.16: 04 - Fatou and Julia sets. pdf
- Class 06, 2019.10.19: 05a - Dynamics on hyperbolic surfaces. pdf
- Class 06-07, 2019.10.19-26: 05b - Tori and Lattes maps. pdf
- Class 07, 2019.10.26: 06a - Contracting and repelling germs. pdf
- Class 08, 2019.11.06: 06b - Tangent to the identity germs, formal classification and flower theorem. pdf
- Class 09, 2019.11.13: 06c - Parabolic germs, topological and analytical classification. pdf
- Class 09, 2019.11.13: 06d - Irrational germs, first results. pdf
- Class 10, 2019.11.16: 06e - Diophantine conditions. pdf
- Class 10, 2019.11.16: 06f - Irrational germs, linearizability and small cycles. pdf
- Class 11, 2018.11.20: 07a - From local to global, attracting case. pdf
- Class 11, 2018.11.20: 07b - From local to global, superattracting case. pdf
- Class 12, 2018.11.27: 07c - From local to global, indifferent case. pdf
- Class 12, 2018.11.27: 08a - Non-repelling vs repelling cycles. pdf
- Class 13, 2018.12.04: 08b - Invariant Fatou components. pdf
- Class 13, 2018.12.04: 09 - Quasiconformal surgery. pdf
- Class 13, 2018.12.04: 10a - Sullivan theorem, Baker's argument. pdf
- Class 14, 2018.12.11: 10b - Sullivan theorem, quasiconformal deformations. pdf
- Class 14, 2018.12.11: 10c - Other applications of quasiconformal surgery. pdf
- Class 15, 2018.12.18: 11 - Potential theory. pdf
- Class 16, 2018.12.25: 12 - Holomorphic families of rational maps. pdf
Some images
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Filled Julia set of f(z)=z^2-0.123+0.745i (Douady's rabbit). |
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Julia set of f(z)=z^2-0.194+0.6557i. |
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Filled Julia set of f(z)=z^3-0.48z+0.706260+0.502896i (Douady's family of rabbits). |
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Julia set of f(z)=z3-0.75z+0.25isqrt10. |
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Mandelbrot set (in black), associated to the family of maps f_c(z)=z^2+c. |
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Julia set and basins of attraction of the Newton method associated to g(z)=z^3-1. |