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CDS 140b

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CDS 140b -- Winter 2010
Second Term

Introduction to Dynamics



CDS 140b is a continuation of CDS 140a. More than half of the course will focus on tools from nonlinear dynamics, such as the existence of periodic orbits, bifurcation theory, chaos, etc. During the second part of the course, guest lecturers will give an introduction to current research topics in dynamical systems theory. There will be three homeworks throughout the semester and a midterm exam. Instead, the students are required to select a research topic and a journal paper related to CD140b and present a brief review of the paper. The details of the projects will be discussed in the class.

Lectures: TR 14:30am-15:55am, 214 Steele.

Instructor: Nader Motee.

Office hours: by appointment.

Teaching Assistant: Molei Tao

Office hours: Wed. 16:00-17:00, Steele 15.

Course Schedule and Lecture Notes:
  • Notes from some of the lectures
  • Week 1: Limit Cycles, Index Theory.
  • Week 2: Poincare-Bendixson Theorem.
  • Week 3: Lienard systems, series expansions for weakly nonlinear systems, Hopf bifurcation.
  • Week 4: Structural stability, Codimension-one Bifurcations
  • Week 5: Unfoldings of Bifurcations, Hopf Bifurcation
  • Week 6: Poincare Map, Stability of Periodic Orbits
Guest Lectures and Final Projects:

Homeworks:

Course Projects: