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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 surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an ...

Wynn's epsilon-method is a method for numerical evaluation of sums and products that samples a number of additional terms in the series and then tries to extrapolate them by ...

Operations research is a vast branch of mathematics which encompasses many diverse areas of minimization and optimization. Thousands of books have been written worldwide on ...

The most general forced form of the Duffing equation is x^..+deltax^.+(betax^3+/-omega_0^2x)=gammacos(omegat+phi). (1) Depending on the parameters chosen, the equation can ...

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 map x_(n+1)=2mux_n, (1) where x is computed modulo 1. A generalized Baker's map can be defined as x_(n+1) = {lambda_ax_n y_n<alpha ; (1-lambda_b)+lambda_bx_n y_n>alpha ...

A dimension also called the fractal dimension, Hausdorff dimension, and Hausdorff-Besicovitch dimension in which nonintegral values are permitted. Objects whose capacity ...

The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

Given a subset S subset R^n and a point x in S, the contingent cone K_S(x) at x with respect to S is defined to be the set K_S(x)={h:d_S^-(x;h)=0} where d_S^- is the upper ...