Spring 2002–2003Ma 4 -
Introduction to Mathematical Chaos |
Midterm Exam (due Mon., May 5 at 5pm): [dvi] [pdf] [ps] Homework:
Objectives: This course is devoted to the study of discrete-time dynamical systems, which arise whenever a function is iterated repeatedly. Common features of these systems include fixed points, attracting or repelling orbits, stable or unstable manifolds, and asymptotic or chaotic behavior. All of these can be produced with relatively simple examples. Describing the general features of a dynamical system only raises new questions: Are these features stable under perturbations? What combinations of features are possible? Is there a well-defined boundary between asymptotic and chaotic regimes? Phenomena such as bifurcation and period-doubling will arise everywhere when we try to answer these questions. The theoretical parts of the course will use elementary ideas from topology, geometry, and calculus. Each new definition will be illustrated by one or more concrete examples and computations. Text: Robert Devaney, An Introduction to chaotic dynamical systems, second edition, 1989. Recommended Reading: Robert Devaney, A first course in chaotic dynamical systems; Theory and experiement, 1992. Grading: Weekly homework 50%, midterm 20%, final 30%. Late work will be accepted only with prior notice and a valid excuse. Collaboration Policy: You may discuss homework problems with other students, but solutions should be written up individually in your own words. Take-home exams must be your own work. |