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A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...

An abstract machine that is implemented in software is termed a virtual machine.

A compact set W_infty with area mu(W_infty)=8/9(24)/(25)(48)/(49)...=pi/4 created by punching a square hole of length 1/3 in the center of a square. In each of the eight ...

The two-dimensional map x_(n+1) = [x_n+nu(1+muy_n)+epsilonnumucos(2pix_n)] (mod 1) (1) y_(n+1) = e^(-Gamma)[y_n+epsiloncos(2pix_n)], (2) where mu=(1-e^(-Gamma))/Gamma (3) ...

An algorithm originally described by Barnsley in 1988. Pick a point at random inside a regular n-gon. Then draw the next point a fraction r of the distance between it and a ...

A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...

A flow defined analogously to the Anosov diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

The best known example of an Anosov diffeomorphism. It is given by the transformation [x_(n+1); y_(n+1)]=[1 1; 1 2][x_n; y_n], (1) where x_(n+1) and y_(n+1) are computed mod ...

Let T be an ergodic endomorphism of the probability space X and let f:X->R be a real-valued measurable function. Then for almost every x in X, we have 1/nsum_(j=1)^nf ...