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A continuous vector bundle is a vector bundle pi:E->M with only the structure of a topological manifold. The map pi is continuous. It has no smooth structure or bundle metric.

Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.

For a two-dimensional map with sigma_2>sigma_1, d_(Lya)=1-(sigma_1)/(sigma_2), where sigma_n are the Lyapunov characteristic exponents.

The nonlinear three-dimensional map X^. = -(Y+Z) (1) Y^. = X+aY (2) Z^. = b+XZ-cZ (3) whose strange attractor is show above for a=0.2, b=0.2, and c=8.0.

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 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. ...

A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define a={0 for theta_b=1/2pi; ...

Also called a chain map. Given two chain complexes C_* and D_*, a chain homomorphism is given by homomorphisms alpha_i:C_i->D_i such that alpha degreespartial_C=partial_D ...

A theorem which effectively describes how lengths, areas, volumes, and generalized n-dimensional volumes (contents) are distorted by differentiable functions. In particular, ...