George Haller: Catalogue data in Spring Semester 2014 |
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 | 3G | 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 | ||||
151-0532-00L | Nonlinear Dynamics and Chaos I | 4 credits | 2V + 1U | G. Haller | |
Abstract | Basic facts about nonlinear systems; stability and near-equilibrium dynamics; bifurcations; dynamical systems on the plane; non-autonomous dynamical systems; chaotic dynamics. | ||||
Objective | This course is intended for Masters and Ph.D. students in engineering sciences, physics and applied mathematics who are interested in the behavior of nonlinear dynamical systems. It offers an introduction to the qualitative study of nonlinear physical phenomena modeled by differential equations or discrete maps. We discuss applications in classical mechanics, electrical engineering, fluid mechanics, and biology. A more advanced Part II of this class is offered every other year. | ||||
Content | (1) Basic facts about nonlinear systems: Existence, uniqueness, and dependence on initial data. (2) Near equilibrium dynamics: Linear and Lyapunov stability (3) Bifurcations of equilibria: Center manifolds, normal forms, and elementary bifurcations (4) Nonlinear dynamical systems on the plane: Phase plane techniques, limit sets, and limit cycles. (5) Time-dependent dynamical systems: Floquet theory, Poincare maps, averaging methods, resonance (6) Chaotic dynamics: Homoclinic dynamics, attractors, Lyapunov exponents | ||||
Lecture notes | The class lecture notes will be posted electronically after each lecture. Students may rely on these or prepare their own notes during the lecture. | ||||
Prerequisites / Notice | The course will be given in English. - Prerequisites: Analysis and a basic course in differential equations. - Exam: two-hour on-line exam in English. - Homework: A homework assignment will be due roughly every other week. Solutions will be posted after the homework due dates. - Grade policy: Up to 10% of the final grade is given for turning in all homework assignments before their due dates. An additional 15% of the final grade is based on one randomly selected homework, which will be graded at the end of the semester. The remaining 75% of the final grade is based on the exam. | ||||
151-1550-00L | Seminar in Mechanics | 0 credits | 2S | J. Dual, C. Glocker, G. Haller, E. Mazza | |
Abstract | Current problems in theoretical, numerical and experimental mechanics from academia and industry. | ||||
Objective | Current problems in theoretical, numerical and experimental mechanics from academia and industry. |