endo

Calculate and graphically display an iterated endomorphism of the plane

Authored and Contributed by: Ronald Joe Record
Description: Endo is an X11 client. The basic idea is to iterate an endomorphism of the plane (R x R). Each point (x,y) is mapped to (f(x,y),g(x,y)). The new point is then mapped to (f(f(x,y),g(x,y)),g(f(x,y),g(x,y))) and so on. Each point is then colored according to how many iterates it took to get within some "delta" of a previous iterate (e.g. a periodic orbit is detected). Lyapunov exponents can be calculated and displayed for a region of parameter space. Phase portraits can be constructed and histographic data displayed. Finally, critical curves and their iterates may be displayed (curves for which the determinant of the Jacobian is zero).
Productivity: This program was designed to assist in the exploration and research of iterated non-invertable maps of the plane. It has proved useful in constructing a phenomenology of the dynamical properties of such maps.
Safety: I have used it for a year without harm.
Work Planned: Improve the Lyapunov exponent algorithm so that both exponents are calculated explicitly.
Documentation: manual page.
Verification: Execute any or all of the shell scripts provided in /usr/skunk/lib/endo.