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A patch (also called a local surface) is a differentiable mapping x:U->R^n, where U is an open subset of R^2. More generally, if A is any subset of R^2, then a map x:A->R^n ...

A map psi:M->M, where M is a manifold, is a finite-to-one factor of a map Psi:X->X if there exists a continuous surjective map pi:X->M such that psi degreespi=pi degreesPsi ...

Let X and Y be CW-complexes, and let f:X->Y be a continuous map. Then the cellular approximation theorem states that any such f is homotopic to a cellular map. In fact, if ...

A special nonsingular map from one manifold to another such that at every point in the domain of the map, the derivative is an injective linear transformation. This is ...

If an integrable quasiperiodic system is slightly perturbed so that it becomes nonintegrable, only a finite number of n-map cycles remain as a result of mode locking. One ...

A term sometimes used to describe a map projection which is neither equal-area nor conformal (Lee 1944; Snyder 1987, p. 4).

A pseudocylindrical map projection which distorts shape, area, scale, and distance to create attractive average projection properties.

A subspace A of X is called a retract of X if there is a continuous map f:X->X (called a retraction) such that for all x in X and all a in A, 1. f(x) in A, and 2. f(a)=a. ...

If f:E->B is a fiber bundle with B a paracompact topological space, then f satisfies the homotopy lifting property with respect to all topological spaces. In other words, if ...

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...