MATH 452 (Introduction to Dynamics and Chaos)
| DESCRIPTION |
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. |
| PREREQUISITES |
Math 246 and either MATH 240 or 461. 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: MATH is cross-listed with AMSC
452. Thus credit will be granted for only one of the
following: AMSC 452, MAPL 452, or MATH 452.
|
| TOPICS |
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
Horseshoe maps
Sensitive dependence
Lyapunov exponents
|
| TEXT |
Text(s)
typically used in this course. |
|
