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A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

Every smooth nonzero vector field on the 3-sphere has at least one closed orbit. The conjecture was proposed in 1950 and proved true for Hopf maps. The conjecture was ...

The set of "critical values" of a map u:R^n->R^n of map class C^1 has Lebesgue measure 0 in R^n.

The study of map projections and the making of geographical maps.

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 ...

A continuous map f:X->Y between topological spaces is said to be null-homotopic if it is homotopic to a constant map. If a space X has the property that id_X, the identity ...

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.

A diffeomorphism is a map between manifolds which is differentiable and has a differentiable inverse.

The associahedron is the n-dimensional generalization of the pentagon. It was discovered by Stasheff in 1963 and it is also known as the Stasheff polytope. The number of ...

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.