**Up:** *Iteration*

# One-Dimensional Dynamical Systems

## Part 3: Iteration

#### Iterates versus time

The most intuitive way of vizualizing an orbit is by plotting the
iterates versus time. Such time series were also produced in
Part 2. Typically, measurements
in experiments form such a time series. A lot of theory in dynamical
systems is developed for constructing a model, i.e. an expression for
the underlying function, out of the measurements.

*Plotting iterates versus time for the Logistic map.*

Iterates versus time can be plotted with the following software. If
you are using a Macintosh computer, follow the instructions for the
software Chaos and Dynamics. On
the other machines, you should follow the instructions for using
Mathematica.

- Use the Java Applet
Iterates versus time for
the Logistic map to see how the plot changes as
varies. Describe what you see.

Note that always the iterates of *x*_{0} = 0.5 are
taken. Can you find values for *x*_{0}
( 0) for
which the orbit behaves differently from *x*_{0} = 0.5?

**Up:** *Iteration*

*The Geometry Center Home Page*
Written by Hinke Osinga

Comments to:
webmaster@geom.umn.edu

Created: Apr 1 1998 ---
Last modified: Thu Apr 9 14:56:17 1998