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# One-Dimensional Dynamical Systems

The study of one-dimensional discrete dynamical systems gives a
new interpretation to the investigation of functions defined on the
real line, and elaborate on the concept of iteration of
functions. Explorations are done using the package
Chaos.m in
Mathematica, or
Chaos and Dynamics (for Macintosh computers), and three
Java applets.

## Table of Contents:

## Java Applets

John McDonald made the Java applet
Iterates versus time for
the Logistic map. You can set the number of iterates being shown
and use sliders to vary the parameter
.

There are two other Java applets available on the web that let you
explore the Logistic map. The applet
Iteration of the Logistic Map of Andy Burbanks has sliders for
changing the parameter
and the starting
point *x*_{0}. See also the
local copy.

The second applet
The Period Doubling Route to Chaos is written by Michael Cross. It
accepts typed input, and it graphs the first, second and fourth
iterates (and so on) of the logistic map.
Complete instructions are given at the site, but you can also
start with the abstracted
instructions that show you how to do everything needed for this
lab.

## References

One-Dimensional Dynamical Systems was designed using

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*The Geometry Center Home Page*
Written by Hinke Osinga

Comments to:
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Created: Mar 31 1998 ---
Last modified: Mon May 18 16:24:26 1998