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The term "fractal dimension" is sometimes used to refer to what is more commonly called the capacity dimension of a fractal (which is, roughly speaking, the exponent D in the ...

A point where a stable and an unstable separatrix (invariant manifold) from the same fixed point or same family intersect. Therefore, the limits lim_(k->infty)f^k(X) and ...

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 ...

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

A hyperbolic fixed point of a differential equation is a fixed point for which the stability matrix has eigenvalues lambda_1<0<lambda_2, also called a saddle point. A ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

An algorithm in control theory introduced by Kalman (1960) and refined by Kalman and Bucy (1961). It is an algorithm which makes optimal use of imprecise data on a linear (or ...

Suppose x_1<x_2<...<x_n are given positive numbers. Let lambda_1, ..., lambda_n>=0 and sum_(j=1)^(n)lambda_j=1. Then ...

A level set in two dimensions. Phase curves are sometimes also known as level curves (Tabor 1989, p. 14).

A regression that is linear in the unknown parameters used in the fit. The most common form of linear regression is least squares fitting. Least squares fitting of lines and ...