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A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

f(x)=1/x-|_1/x_| for x in [0,1], where |_x_| is the floor function. The natural invariant of the map is rho(y)=1/((1+y)ln2).

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

The general displacement of a rigid body (or coordinate frame) with one point fixed is a rotation about some axis. Furthermore, a rotation may be described in any basis using ...

Let phi be a map. Then phi is expansive if the statement that the distance d(phi^nx,phi^ny)<delta for all n in Z implies that x=y. Equivalently, phi is expansive if the ...

A map psi:M->M, where M is a manifold, is a finite-to-one factor of a map Psi:X->X if there exists a continuous surjective map pi:X->M such that psi degreespi=pi degreesPsi ...

A product of a reflection in a line and translation along the same line.

Also known as the a Lorentz transformation or Procrustian stretch, a hyperbolic transformation leaves each branch of the hyperbola x^'y^'=xy invariant and transforms circles ...

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...