國立清華大學數學系
Math 5313 (Spring 2006)
動態系統導論二
Introduction to Dynamical Systems (II)
General
Information
Hours and Days: W3W4F4 (i.e.
Classroom: 綜三 606
Instructor: 陳 國 璋
Office: 綜三 609
Office Hours: T3T4, or by appointments
Phone Number: (03) 5715131 Ext: 33067
Email: kchen@math.nthu.edu.tw
Prerequisite: Differential equations and real analysis (or measure theory). Math
5312 (Introduction to Dynamical Systems (I)) is recommended but not absolutely
necessary.
Textbooks/References:
1. Alligood, Sauer, Yorke: Chaos: An Introduction to Dynamical Systems,
Springer, 1996.
2. Brin, Stuck: Introduction to Dynamical Systems,
3. Robinson: Dynamical Systems - Stability, Symbolic Dynamics, and Chaos,
CRC Press, 1999.
4. Pollicott, Yuri: Dynamical Systems and Ergodic Theory,
Course Description
The theory of dynamical systems is a major
mathematical discipline connecting with various fields, including geometry,
probability, number theory, physics, biology, economics,
among many others. Its main goal is to understand the evolution and long term
behavior of time dependent systems. The time variable is either discrete or
continuous, and the law of evolution can be deterministic or stochastic. Many
simple nonlinear systems are known to exhibit surprisingly chaotic dynamics
that cannot be anticipated by linear analysis.
In the second semester of this introductory course we will cover the following
topics:
1. Dynamics near periodic orbits
2. Fractals
3. Measurements of chaos
4. Bifurcations
5. Hyperbolic invariant sets (if time permits)
Grading
Homework Assignments (60%): There will be 4 homework assignments.
Final Report (40%): A written report and/or oral
presentation during the final week.