Remus Radu

Synopsis

Dynamical systems occur in all branches of science, from the differential equations of classical mechanics in physics to the difference equations of mathematical economics and biology. This course is an introduction to the field of dynamical systems. It concerns the study of the long-term behavior of solutions to ordinary differential equations or of iterated mappings, emphasizing the distinction between stability on the one hand and sensitive dependence and chaotic behavior on the other. The course describes examples of chaotic behavior and of fractal attractors, and develops some mathematical tools for understanding them. In particular we will study the following key concepts: hyperbolicity, topological conjugacy, equilibrium, limit cycle, stability, chaos, etc.

Click here to download a copy of the course syllabus. Please visit the course website on Blackboard to see your grades.

Lectures

Tuesday & Thursday 1:00-2:20pm in Physics 116

Instructor

Remus Radu
Office: Math Tower 4-103
Office hours: TuTh 2:30-4:00pm in Math Tower 4-103, or by appointment

Teaching Assistant

Aleksandar Milivojevic
Office: MLC (Math Tower S-240A)
Office hours: Monday 10:00-11:00am & 1:00-2:00pm; Wednesday 10:30-11:30am in MLC

Textbook & recommended reading

• Steven Strogatz, Nonlinear dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, Westview press.
• Wei-bin Zhang, Differential equations, bifurcations, and Chaos in economics, World Scientific 2005.
• Robert L. Devaney, Morris W. Hirsch, and Stephen Smale, Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3rd ed., Elsevier Academic Press, 2012.
• Robert L. Devaney, A First Course in Chaotic Dynamical Systems: Theory And Experiment, Westview Press 1992.
• Clark Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, 2nd ed., CRC Press. (more advanced)
• John Guckenheimer, Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer 1983. (more advanced)
*** We will follow the first three textbooks, but there will also be lecture notes posted on Blackboard. ***

Grading Policy

Grades will be computed using the following scheme:

• Homework – 30%
• Midterm – 35% (on Thursday, March 31, 1:00-2:20pm)
• Projects & presentation – 35%

Students are expected to attend class regularly and to keep up with the material presented in the lecture and the assigned reading.