# Readings

## Books

The most important book, which we recommend that you purchase, is:

Strogatz, S. *Nonlinear Dynamics and Chaos*. Reading, MA: Addison-Wesley, 1994. ISBN: 0201543443.

Strogatz will be especially valuable for our discussion of stability of ordinary differential equations.

In our discussions of data analysis techniques, the following book may be useful:

Baker, G. L., and J. P. Gollub. *Chaotic Dynamics*. 2nd ed. New York, NY: Cambridge University Press, 1996. ISBN: 0521471060 (hardback).

Also of interest, due to its elementary and physical presentation, is:

Berg´e, P., Y. Pomeau, and C. Vidal. *Order Within Chaos*. New York, NY: John Wiley & Sons, 1984. ISBN: 0471849677.

Among the many books on chaos, fractals, pattern formation, and related mathematics, you may find it interesting to consult, either during or after the course, the following:

Beltrami, E. *Mathematics for Dynamic Modeling.* Boston, MA: Academic Press, 1987. ISBN: 0120855550.

An elementary presentation of many of the mathematical techniques useful in studying dynamics. Especially useful for a review of ordinary differential equations, stability, fixed points, and phase space representations.

Cvitanovi´c, P., ed. *Universality in Chaos.* Bristol, UK: Adam Hilger Ltd., 1984. ISBN: 0852747659 (paperback), 0852747667 (hardback).

Contains reprints of a number of original research papers in the field.

Gleick, James. *Chaos: Making a New Science / James Gleick.* New York, NY, U.S.A.: Viking, 1987. ISBN: 0670811785.

An excellent popular introduction to the subject for the lay reader.

Guckenheimer, John, and Philip Holmes. *Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields.* New York, NY: Springer-Verlag, c1983. ISBN: 0387908196.

A graduate-level applied mathematics text.

Hilborn, Robert C. *Chaos and Nonlinear Dynamics.* New York, NY: Oxford University Press, 1994. ISBN: 0195057600.

One of the more elementary and better recent books on the subject, oriented more for the physicist than for the mathematician. Big (over 600 pages). Lots of good exercises.

Kaplan, D., and L. Glass. *Understanding Nonlinear Dynamics.* New York, NY: Springer-Verlag, 1995. ISBN: 0387944400.

A nice undergraduate-level introduction, oriented towards scientists, and especially biologists.

Manneville, P. *Dissipative Structures and Weak Turbulence.* Boston, MA: Academic Press, 1990. ISBN: 0124692605.

Covers the low-dimensional theory discussed in the course but also includes considerable discussion of recent research on spatially-extended systems. Advanced.

Schuster, H. G. *Deterministic Chaos.* 2nd ed. New York, NY: VCH, 1988. ISBN: 3527268626.

An advanced book of interest to physicists.

Thompson, J. M. T., and H. B. Stewart. *Nonlinear Dynamics and Chaos.* New York, NY: John Wiley & Sons, 1986. ISBN: 0471909602.

A textbook of moderate difficulty with lots of nice pictures and a fair amount of material of engineering interest.

Turcotte, D. *Fractals and Chaos in Geology and Geophysics.* 2nd ed. New York, NY: Cambridge University Press, 1997. ISBN: 0521561647.

Provides a number of nice examples of nonlinear phenomena in the earth sciences.