151-0530-00L Nonlinear Dynamics and Chaos II
| Semester | Spring Semester 2023 |
| Lecturers | G. Haller |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| 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 |