Search Results for ""

A surface (or "space") of section, also called a Poincaré section (Rasband 1990, pp. 7 and 93-94), is a way of presenting a trajectory in n-dimensional phase space in an ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

A fixed point is a point that does not change upon application of a map, system of differential equations, etc. In particular, a fixed point of a function f(x) is a point x_0 ...

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

A vector field v for which the curl vanishes, del xv=0.

The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A ...

An area-preserving affine transformation. Equiaffinities include the crossed hyperbolic rotation, elliptic rotation, hyperbolic rotation, and parabolic rotation.

The boundary of complex hyperbolic 2-space.