Brief Course Description: This is the first semester of a two semester sequence of courses on Ergodic Theory and Dynamical Systems. The first semester studies topological and differential properties of evolving systems, or more precisely, of the orbits of differential equations and iterated functions. Dynamical Systems forms the mathematical foundations of what is popularly known as "Chaos Theory". The second semester focuses on Ergodic Theory which studies the statistical properties of the evolution of complex systems. The two semesters are independent.
The first semester course will cover the basics of Topological and Differentiable Dynamics including minimal sets and various kinds of recurrence, the smooth theory of the dynamics of circle diffeomorphisms, kneading theory and the quadratic family, symbolic dynamics and the standard examples of chaotic dynamics such as Smale's Horseshoe and the Lorenz Attractor.
Prerequisites: A knowledge of metric space topology (eg. from Rudin's Principles of Mathematical Analysis) and a solid course in multi-variable (advanced) calculus. Otherwise the course will be self-sufficient.
Text: The course will be based on class notes, but will somewhat follow Introduction to Dynamical Systems by Michael Brin and Garrett Stuck, and so that is an optional textbook.
Grades: Grades will be based on homework and a final exam. Homework will be assigned each Friday and is due the next Friday. Late homework may be turned in the next Monday for 2/3 credit. No homework is accpted after the start of class on Monday. No email submissions of nomework will be accepted. The Final Exam will cover the whole course, will be 2 hours and open notes.
Excused Absences: In certain circumstances a student will be able to make up a missed exam. These circumstances could include medical situations, family emergencies, travel for University activities (eg. band, debating club, etc), and religious observances. In these cases the student must inform me before or within one week after the missed work and provide written documentation.
Honor Code: On all work submitted for credit by students at the university, the following pledge is either required or implied:
On my honor, I have neither given nor received unauthorized aid in doing this assignment.
For more information on the student honor code see the Dean of Students Website.
Accommodations for Students with Disabilities: The University Policy: "Students requesting classroom accommodation must first register with the Dean of Students Office. The Dean of Students Office will provide documentation to the student who must then provide this documentation to the Instructor when requesting accommodation."