Dynamical Systems and Chaos

Evans M. Harrell II

(c) Copyright 1992, 1997, 2000 by Evans M. Harrell II. All rights reserved.

These are class notes written by Evans M. Harrell II of Georgia Tech. They are suitable for an introductory course on dynamical systems and chaos, taken by mathematicians, engineers, and physicists. Students are expected to have completed two years of calculus and basic courses on ordinary differential equations, linear algebra, and analysis.

This text concentrates on models rather than proofs in order to bring out the concepts of dynamics and chaos. Theorems are carefully stated, though only occasionally proved.

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Contents


I.    Introduction
II.   Phase portraits
III.   Iterated maps.
IV.   Recurrence.
V.    Symbolic dynamics.
VI.   Lyapunov exponents.
VII.  Ergodic motion.
VIII. Intermittency.
  Bibliography
A suitable final examination

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