Iterations of the complex Henon map.

This page introduces a Java applet which allows one to investigate orbits of certain complex Henon maps. A preprint "Reversible complex Henon maps" by C.R. Jordan, D.A. Jordan and J.H. Jordan giving more detail is available as a pdf file.

The complex Henon map is a map H from two-dimensional complex space to itself involving two parameters a and b:

H

z
w


=

a-bw-z2
z


.

The case in which we are interested is when b has modulus 1 and a=rb is a real multiple of b. In this case H can be written as the composition of two involutions.

The applet allows you to choose the parameters r and q (the argument of b) either graphically or numerically.

Choosing the parameters graphically

Choosing the parameters numerically.

Changing the starting point of the orbit.

Colouring

Scale etc.

The other buttons enable you to zoom in or out from an orbit, or move about the screen. The new orbit is replotted from scratch each time. "Clear" removes all orbits and "Reset" clears the orbits and puts the screen parameters back to their initial values.

If you have any comments, such as problems running the applet or the discovery of amazing orbits, please let me know by email.

Another version of the applet is an appendix to the preprint and contains instructions similar to those above but with references to the preprint.


File translated from TEX by TTH, version 1.67.