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A characteristic of some systems making a transition to chaos. Doubling is followed by quadrupling, etc. An example of a map displaying period doubling is the logistic map.

A string or word is said to be admissible if that word appears in a given sequence. For example, in the sequence aabaabaabaabaab..., a, aa, baab are all admissible, but bb is ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

Calculus II

In a dynamical system, a bifurcation is a period doubling, quadrupling, etc., that accompanies the onset of chaos. It represents the sudden appearance of a qualitatively ...

Given ∠AXB+∠AYB=pi radians in the above figure, then X and Y are said to be antigonal points with respect to A and B.

If a map f:G->G^' from a group G to a group G^' satisfies f(ab)=f(b)f(a) for all a,b in G, then f is said to be an antihomomorphism.

The number of elements of a group in a given conjugacy class.

A relation R on a set S is irreflexive provided that no element is related to itself; in other words, xRx for no x in S.

A homogeneous polynomial in two or more variables.