George Haller: Catalogue data in Spring Semester 2019 |
| Name | Prof. Dr. George Haller |
| Field | Nonlinear Dynamics |
| Address | Chair in Nonlinear Dynamics ETH Zürich, LEE M 210 Leonhardstrasse 21 8092 Zürich SWITZERLAND |
| Telephone | +41 44 633 82 50 |
| georgehaller@ethz.ch | |
| URL | http://georgehaller.com |
| Department | Mechanical and Process Engineering |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 151-0530-00L | Nonlinear Dynamics and Chaos II  Does not take place this semester. | 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 | ||||
| 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 | Students have to prepare their own lecture notes | ||||
| Literature | Books will be recommended in class | ||||
| Prerequisites / Notice | Nonlinear Dynamics I (151-0532-00) or equivalent | ||||