Details of MA5221 (Spring 2026)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA5221 | Complex Dynamics I | Sushil Gorai |
| Syllabus |
|---|
| Normal families: The Riemann sphere, holomorphic covering maps and Poincare metric, statement of the uniformization theorem, Normal families and Montel's theorem.
Iteration of rational maps: Fatou and Julia sets, periodic points, classification of periodic points Local fixed point theory: Geometrically attracting or repelling fixed points, Koenigs linearization, properties of immediate basin of attracting fixed points; Supper attracting fixed points, Bottcher's theorem, polynomial dynamics near the point at infinity; parabolic fixed points, the Leau-Fatou flower; Cremer points and Siegel discs. Dynamics near periodic points and global theory: attracting cycles, Repelling cycles, rationally indifferent cycles, irrationally indifferent cycles The dynamics of quadratic polynomials and the Mandelbrot set. |
| Prerequisite |
|---|
| MA4201 (Complex analysis) |
| References |
|---|
| References:
1) Alan F. Beardon, Iteration of Rational Functions, Springer 2) John Milnor, Dynamics in One Complex Variable, third edition, Annals of Mathematics Studies 3) S. Morosawa, Y. Nishimura, M. Taniguchi and T. Ueda, Holomorphic Dynamics, Cambridge University Press |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | MP | 2 | Not Allowed |
| 4 | MP | 4 | Elective |
| 5 | MR | 2 | Not Allowed |
| 6 | MR | 4 | Not Allowed |
| 7 | MS | 10 | Elective |
| 8 | MS | 4 | Not Allowed |
| 9 | MS | 6 | Not Allowed |
| 10 | MS | 8 | Elective |
| 11 | RS | 1 | Elective |
| 12 | RS | 2 | Elective |