COURSE SYLLABUS

Course Number: MATH6480
Course Title: DYNAMICAL SYSTEMS II
Credit Hours: 3
Prerequisites: MATH6470
Corequisite: 

Objectives: 
To familiarize the student with the dynamical concepts, first as they relate to classical differential equations and more particularly as these concepts have shown new relevance since the mid 1970's of certain notions from topology, and have developed a mathematical life of their own.

Schedule and Outline of Course Content: 
I. Real higher dimensional dynamics  (4 days).   
   1. Dynamics of linear maps in dimensions two and three  (4 days).
   2. The horseshoe map  (4 days).
   3. Attractors  (4 days).
   4. Stable and unstable manifolds  (4 days).
   5.The Hopf bifurcation (4 days).
II. Complex dynamics
   6.Normal families (4 days).
   7. Periodic points (4 days).
   8. The Julia set (4 days).
   9. The Mandelbrot set. (4 days).

Possible textbooks:
	An Introduction to Chaotic Dynamical Systems by R. L. Devaney.

Grading and Evaluation Procedures: 
Quizzes, tests, midterm exam, final exam. Other methods of evaluation are used at the discretion of the instructor.

Statement related to policies on unannounced quizzes and class attendance and participation:
Individual instructors have different policies concerning pop quizzes, class participation, homework grades, and attendance, which are announced at the beginning of the semester.