Search Results for ""

Consider the circle map. If K is nonzero, then the motion is periodic in some finite region surrounding each rational Omega. This execution of periodic motion in response to ...

There are a number of algebraic equations known as the icosahedral equation, all of which derive from the projective geometry of the icosahedron. Consider an icosahedron ...

An algebraic manifold is another name for a smooth algebraic variety. It can be covered by coordinate charts so that the transition functions are given by rational functions. ...

A compactification of a topological space X is a larger space Y containing X which is also compact. The smallest compactification is the one-point compactification. For ...

Two mathematical objects are said to be homotopic if one can be continuously deformed into the other. For example, the real line is homotopic to a single point, as is any ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

A hyperbolic linear map R^n->R^n with integer entries in the transformation matrix and determinant +/-1 is an Anosov diffeomorphism of the n-torus, called an Anosov ...

Let G=SL(n,C). If lambda in Z^n is the highest weight of an irreducible holomorphic representation V of G, (i.e., lambda is a dominant integral weight), then the G-map ...

A section of a fiber bundle gives an element of the fiber over every point in B. Usually it is described as a map s:B->E such that pi degreess is the identity on B. A ...

A representation of a C^*-algebra A is a pair (H,phi) where H is a Hilbert space and phi:A->B(H) is a *-homomorphism. (H,phi) is said to be faithful if phi is injective. For ...