In this talk we show some of the problems that can occur with this method, and in particular how the largest Lyapunov exponent can be miscalculated in this way. Several methods for controlling chaotic behavior have been developed over the last few years. One technique that can be used to effect the dynamics of a nonlinear system is to drive periodically some system parameter. This technique has been implemented numerically over a wide range of perturbation amplitudes and frequencies on several chaotic systems, including the logistic equation, the Lorenz equations, the Yoshida equations, and coupled map lattices. Cases have been found in which the chaotic behavior can be eliminated at certain perturbation frequencies with very small amplitude perturbations, but the overall occurence of chaotic solutions is not greatly diminished.
Butterfly wings are exceptional in the complexity and diversity of their color patterns.
I will discuss genetic and developmental aspects of wing patterns and the modification of developmental pathways in evolution. Robert L. Wilson, UW Mathematics. Commercially this technology is being used for image compression. An IFS is abstractly a collection of functions which map a space into itself, with restrictions on the space and on how the functions move points around. Applied repeatedly, in a deterministic or a random way, the functions collectively have a fixed set which acts as an attractor.