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Exchanges branches of the hyperbola x^'y^'=xy. x^' = mu^(-1)x (1) y^' = -muy. (2)

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

The order of the polynomial defining an algebraic curve.

A metric g_(ij) which is zero for i!=j.

The operator D=-i(d+d^*), where d^* is the adjoint.

Of opposite symmetry under reflection; mirror images.

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

If an infinite number of points in the plane are all separated by integer distances, then all the points lie on a straight line.

A transformation which has only trivial invariant subsets is said to be ergodic.

The function f(beta,z)|->z^((1+cosbeta+isinbeta)/2), illustrated above for beta=0.4.