MATH759 INTRODUCTION TO CHAOTIC DYNAMICAL SYSTEMS
| Course Code: |
2360759 |
| METU Credit (Theoretical-Laboratory hours/week): |
3(3-0) |
| ECTS Credit: |
8.0 |
| Department: |
Mathematics |
| Language of Instruction: |
English |
| Level of Study: |
Masters |
| Course Coordinator: |
Prof.Dr. MARAT AKHMET |
| Offered Semester: |
Fall or Spring Semesters. |
Course Content
Mappings and Orbits. Periodic orbits. Linear mappings. Differentiable mappings. Fixed points and periodic points. Eventually periodic points. Family of mappings: Bifurcations. The quadratic map. Symbolic dynamics. Ingredients of chaos: Sensitivity. Dense orbits and transitivity. Schwarzian derivatives. Wiggly iterates. Cantor set and chaos. The logistic map. Period-three points and chaos. Period-doubling bifurcation: method of bifurcation diagrams. Positive Lyapunov exponents. The Two-dimensional chaos: the Henon map. the horseshoe map. Alpha unpredictability. Ultra Poincaré chaos. Alpha labeling. Abstract similarity map. Abstract similarity sets. Chaos in stochastic processes. Homoclinic chaos. Hyberbolicity and chaos.
