Orbits of reversible complex Hénon maps
The image which appears on the left side of the applet below shows (in black) the set
B from Figure 6.
Choosing the parameters graphically.
Click with the mouse on the
image of B. The values of r and q,
expressed as a multiple of p,
will appear in the appropriate boxes.
Choosing the parameters numerically.
Please note that numbers must be entered in decimal format.
- Before values can be entered, any previous orbit must
be cleared using the "Clear" button.
- Enter the desired value of r into the r box.
- Enter the desired multiple of p for q into the theta box. A cross will appear on the left side
of the applet to indicate the position of a.
Plotting the orbit.
Click on the button "Plot Orbit" and the first
20,000 points of the orbit, starting from (0,0), will be plotted on the right of the applet,
unless the orbit is found to be unbounded. To plot a further 20,000 points,
click on "Plot Orbit" again. Plotting stops as soon as the
orbit is known to be unbounded by Proposition 5.2.
Selecting coset orbits.
Coset orbits can be coloured
using the "No. of cosets" box. If, for example you enter 4 in this box,
the orbit will appear as 4 coset orbits differently coloured.
Try theta as .3333333 and enter 6 in this box to see the effect.
Up to 235 colours can be used.
If you enter a number k, say, other than 0, in the "Coset to plot" box
then only the kth coset orbit will be plotted.
The other buttons enable you to zoom in or out, or move about
the screen. The 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.
Changing the starting point of the orbit.
- Plot an orbit starting from (0,0).
- "Clear" if you wish.
- Click in the right hand area of the window. This chooses z.
w is set to bz. The message
"Ready to start plotting at ¼" will appear in the status bar.
- Click on "Plot Orbit".
- "Clear" always resets (z,w) to (0,0).