COURSE SYLLABUS Course Number: MATH6470 Course Title: DYNAMICAL SYSTEMS I Credit Hours: 3 Prerequisites: MATH2650 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: 1. Continuous and discrete dynamical systems (4 days). 2. The quadratic family (4 days). 3. Symbolic dynamics (4 days). 4. Topological conjugacy (4 days). 5. Chaos (4 days). 6. Sarkovskii's Theorem (4 days). 7. Bifurcation theory (4 days). 8. Maps of the circle (4 days). 9. Homoclinic points (4 days). 10. The kneading theory (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.