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Refer to the above figures. Let X be the point of intersection, with X^' ahead of X on one manifold and X^('') ahead of X of the other. The mapping of each of these points ...

Isolated resonances in a dynamical system can cause considerable distortion of preserved tori in their neighborhood, but they do not introduce any chaos into a system. ...

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the ...

The Lorenz attractor is an attractor that arises in a simplified system of equations describing the two-dimensional flow of fluid of uniform depth H, with an imposed ...

A two-dimensional binary (k=2) totalistic cellular automaton with a von Neumann neighborhood of range r=1. It has a birth rule that at least 2 of its 4 neighbors are alive, ...

There are two curves known as the butterfly curve. The first is the sextic plane curve given by the implicit equation y^6=x^2-x^6 (1) (Cundy and Rollett 1989, p. 72; left ...

Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

Chebyshev noticed that the remainder upon dividing the primes by 4 gives 3 more often than 1, as plotted above in the left figure. Similarly, dividing the primes by 3 gives 2 ...

A collection of identities which hold on a Kähler manifold, also called the Hodge identities. Let omega be a Kähler form, d=partial+partial^_ be the exterior derivative, ...