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The smallest number of times u(K) a knot K must be passed through itself to untie it. Lower bounds can be computed using relatively straightforward techniques, but it is in ...

A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.

The attractor of the iterated function system given by the set of "fern functions" f_1(x,y) = [0.85 0.04; -0.04 0.85][x; y]+[0.00; 1.60] (1) f_2(x,y) = [-0.15 0.28; 0.26 ...

The longstanding conjecture that the nonimaginary solutions E_n of zeta(1/2+iE_n)=0, (1) where zeta(z) is the Riemann zeta function, are the eigenvalues of an "appropriate" ...

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, ...

A Julia set J consisting of a set of isolated points which is formed by taking a point outside an underlying set M (e.g., the Mandelbrot set). If the point is outside but ...

A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

The bifurcation of a fixed point to a limit cycle (Tabor 1989).

An invariant set S subset R^n is said to be a C^r (r>=1) invariant manifold if S has the structure of a C^r differentiable manifold (Wiggins 1990, p. 14). When stable and ...