Search result: Catalogue data in Spring Semester 2023
Mathematics Master  | ||||||
 Electives (Direction Applied Mathematics MSc Only)Electives from applied mathematics and further application-oriented fields that are only eligible for credits for the Master's degree in Applied Mathematics. | ||||||
| Number | Title | Type | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|---|
| 151-0530-00L | Nonlinear Dynamics and Chaos II | W | 4 credits | 4G | G. Haller | |
| Abstract | The internal structure of chaos; Hamiltonian dynamical systems; Normally hyperbolic invariant manifolds; Geometric singular perturbation theory; Finite-time dynamical systems | |||||
| Learning objective | The course introduces the student to advanced, comtemporary concepts of nonlinear dynamical systems analysis. | |||||
| Content | I. The internal structure of chaos: symbolic dynamics, Bernoulli shift map, sub-shifts of finite type; chaos is numerical iterations. II.Hamiltonian dynamical systems: conservation and recurrence, stability of fixed points, integrable systems, invariant tori, Liouville-Arnold-Jost Theorem, KAM theory. III. Normally hyperbolic invariant manifolds: Crash course on differentiable manifolds, existence, persistence, and smoothness, applications. IV. Geometric singular perturbation theory: slow manifolds and their stability, physical examples. V. Finite-time dynamical system; detecting Invariant manifolds and coherent structures in finite-time flows | |||||
| Lecture notes | Handwritten instructor's notes and typed lecture notes will be downloadable from Moodle. | |||||
| Literature | Books will be recommended in class | |||||
| Prerequisites / Notice | Nonlinear Dynamics I (151-0532-00) or equivalent | |||||
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