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The problem of deciding if two knots in three-space are equivalent such that one can be continuously deformed into another.

A knot diagram which does not specify whether crossings are under- or overcrossings.

S_n=sum_(i)eta_imu(E_i), where mu(E_i) is the measure of the set E_i of points on the x-axis for which f(x) approx eta_i.

An attracting set to which orbits or trajectories converge and upon which trajectories are periodic.

Always increasing; never remaining constant or decreasing. Also called strictly increasing.

An element B of a ring is nilpotent if there exists a positive integer k for which B^k=0.

A vector space possessing a norm.

A function f:A->B such that B is a set of numbers.

The ring R[x] of polynomials in a variable x.

Predictability at a time tau in the future is defined by (R(x(t),x(t+tau)))/(H(x(t))), and linear predictability by (L(x(t),x(t+tau)))/(H(x(t))), where R and L are the ...