MATH 452 is a one semester introduction to dynamics and chaos. The course focuses on the basic structures of one and two dimensional dynamical systems and families of systems. Below is listed the core topics of the course. The instructor should feel free to augment this basic material with more advanced subjects.
MATH 246 and (MATH 240 or MATH 461); or MATH341. It is also recommended that the student have some additional 400 level courses in Mathematics, Science, or Engineering. (In some classes, each student will develop a project usually involving numerical investigations.) Note: Also listed as AMSC 452.
One and Two Dimensional Dynamics
Fixed and periodic points
Families of functions and bifurcation
The Li-Yorke theorem and Sarkovskii's theorem
Stable and unstable manifolds