The purpose of this movie is to see the evolution of the period five
islands in the H\'enon conservative map, from a parameter value close
to the birth of the islands, near the central elliptic point, to a
parameter value after the destruction of these islands.
The version of the H\'enon map used here is
(x,y) --> (X,Y), Y=y+c(1-(x+y)^2)/2, X=x+y+Y,
where c is the current parameter of the map.
To see movie1 you must do
1) to compile the program movie1.f
for instance, if you are using linux you can compile it by typing
gfortran -funroll-loops -ffast-math -O2 -Wall movie1.f -o movie1.xxx
2) then, if you start by typing ./movie1.xxx the program reads the
precomputed data in data1.pre, makes some iterations of the map with
several initial points, all of them located on the x axis and plots
the results.
To this end it invokes automatically gnuplot with the command file
movie1.gnu. In this file there are some definitions of size and
location of the window. It is possible to change them by editing the
movie1.gnu file. Also note that the files to be plotted can be not
so small (20 o more Mb). It can take a few seconds to compute and
display each figure, depending on the computer.
On the window where you started the program it displays the value
used for the parameter of the map, the number of initial data for
which the orbit is detected to be regular and the number of initial
data for which the orbit is detected to be chaotic.
Points in regular orbits are plotted in red while points in chaotic
orbits are plotted in green.
3) after each plot, return to the window where you started the program
and press return to proceed to the new parameter value. At the end of
the plots it gives also, in seconds, the total time spent in the
computations. All the intermediate files are erased at the end.
Enjoy the evolution of the islands!