ALEA::HENON-HEILLES
Arguments: xinit yinit ydot e dt pas [generic-function]
This system was originally introduced as a simplified model of the individual movement of a star within a grav-itational field:
dx^2/dt^2= -x-2xy dy^2/dt^2= -y+y^2-x^2 where x and y are the starÕs coordinates, E is the total energy of the system, The maximum permitted value for E is 1/6. - xinit, yinit and ydot are the initial values; - E is the value of the total energy; - dt is a value of time for the numerical integration in the equations; - pas is the number of iterations, or generated points. The output of this module is a [[list]] of coordinates in four dimensions : ((xinit yinit xdot ydot ) (x0 y0 xdot0 ydot0 ) (x1 x2 xdot1 ydot2 ) ... (xn yn xdotn ydotn )). The [[second]] output returns a x values list, the [[third]] input returns a y values list, the fourth output returns a xdot values list and the fifth output returns a ydot values list See Rick Bidlack, 1992, Chaotic Systems as Simple (but Complex) compositional Algorithms, in CMJ vol16,n¡3. And Robert H. G. Helleman (1980) -SELF-GENERATED CHAOTIC BEHAVIOR IN NONLINEAR MECHANICS- in Fundamentals Problems in Statistical Mechanics vol 5 pp 165-233.
