An installation instruction of the program realizing the proof of the existence of cocoon bifurcations in the Michelson system as described in paper
H. Kokubu, D. Wilczak and P. Zgliczyński
"Rigorous verification of cocoon bifurcations in the Michelson system"

IMPORTANT:

The program requires gcc-3.4 or newer. It can be compile and run under gcc-3.3, however the option -frounding-math must be removed from the first line of makefile. Earlier versions of gcc are not supported.

GRAPHICS:

The program must be run in the graphics mode. The minimal resolution required is 1024x768. In the case of smaller resolution only a part of the screen will be visible.

Installation instruction under linux with wxWidgets graphics library (recommended):

We tested the program under kubuntu 7.10, gcc-4.2.1. If you have installed wxGTK and wxGTK-devel (just try 'wx-config' command):

please unpack the archive
tar xvfz cocoon.tgz

change directory to 'cocoon' and call 'make'.
cd cocoon
make target=wx
The last command generates an executable file cocoon in the current directory.

We may run the program
./cocoon

Installation instruction under linux with standard X graphics:

We tested the program under several Linux distributions:

Fedora 4, gcc-3.4.2
Mandriva 2006, gcc-4.0.1
Ubuntu 2008, gcc-4.3.2

please unpack the archive
tar xvfz cocoon.tgz

change directory to 'cocoon' and call 'make'.
cd cocoon
make
The last command generates an executable file cocoon in the current directory.

We may run the program
./cocoon

Installation instruction under MS Windows with MinGW compiler:

The program has been tested under MS Windows XP Professional with gcc 3.4.4 compiler. We use the MinGW compiler (Minimalist GNU for Windows - http://www.mingw.org).

please unpack the archive (using for example Total Commander)

change directory to 'cocoon' and call 'mingw32-make'.
cd cocoon
mingw32-make target=win

cocoon.exe

OUTPUT:

file BifurcationPoint.txt with rigorous bound of the Newton operator used in the proof of the existence of saddle-node periodic orbit
file C2BoundOnTrapezoid.txt with rigorous bound of the hessian of Poincare Map on a trapezoid - used in the proof of the existence of a Lyapunov function
file LyapunovFunctionOnH1.txt with rigorous estimation od delta for which P₁(v1,v2)-v1 < -delta for (v1,v2) from the set H1
file LyapunovFunctionOnH2.txt with rigorous estimation od delta for which P₁(v1,v2)-v1 < -delta for (v1,v2) from the set H2
file DP_atBifPoint.txt - rigorous bound for the derivative of the Poincare Map at the bifurcation point

NOTE:

More informations about libraries can be found on the web page of CAPD group: http://capd.ii.uj.edu.pl.