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.

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.

Scale etc.

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.