Back to Courses Catalog CDS 140b

CDS 140b -- Winter 2008 Second Term Introduction to Dynamics CDS 140b is a continuation of CDS 140a. Half of the course will be devoted to covering basic tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, chaos, and Hamiltonian systems. During the second part of the course, guest lecturers will give an introduction to current research topics in dynamical systems theory. Homeworks will be posted on a weekly basis and are due on the date given. There will be a midterm exam but no final. Instead, the students are asked to show their insight in the material covered in class by commenting on a journal paper. Details can be found below. Lectures: TR 10:30am-11:55am, 214 Steele. Instructor: Joris Vankerschaver. Office hours: by appointment. Teaching Assistant: Molei Tao. Office hours: Monday 11:45-12:45. Summary and Lecture Notes: Week 1: Introduction, periodic orbits, Floquet theory, index theory. Week 2: Limit cycles, the Poincare-Bendixson theorem. Week 3: Lienard equations, series expansions for weakly nonlinear systems. Week 4: Structural stability, genericity, 1D bifurcations. Week 5: Simple bifurcations, unfoldings, the Hopf bifurcation. A concise summary of the material covered in class, with references to the literature, can be found below: Periodic orbits. Structural stability and bifurcation theory. The Poincare-Lindstedt method applied to the van der Pol oscillator. The Midterm will be a take-home exam covering the material in weeks 1-5, handed out on Tuesday February 17, and due the next week on Monday, February 23. The exam time is three hours and no aids are permitted. Guest Lectures and Final Project: Week 6 (02/10, 02/12): Hamiltonian Systems. Lecture 1 Project Ideas Week 7 (02/17, 02/19). Sujit Nair: Nonlinear control theory. Week 8 (02/24, 02/26). Philip Du Toit: Lagrangian coherent structures. Project Ideas Week 9 (03/03, 03/05). Dennice Gayme: Transient growth and applications. For the final project, the idea is that you choose a topic during one of the guest lectures, and that you write a short summary of it demonstrating the insight into the subject matter. You are also free to suggest a topic of your own choosing, provided there is a clear link with dynamical systems theory and CDS-140b. The suggested size for the written report is four pages, though more is allowed when you think it is appropriate. The due date for the project paper is Tuesday, March 10. It is strongly suggested that you write the paper in LaTeX and submit it via email to jv@caltech.edu. Homeworks: Homework 1. Due 01/20. Homework 2. Due 01/29. Homework 3. Due 02/10. References: The reference works for this class are listed in the course notes. If you cannot find a book in the CDS library, contact me.