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For any two ergodic measure-preserving transformations on nonatomic probability spaces, there is an isomorphism between the two probability spaces carrying orbits onto orbits.

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

An affine transformation that preserves area.

A symmetry group is a group of symmetry-preserving operations, i.e., rotations, reflections, and inversions (Arfken 1985, p. 245).

Let phi(z)=cz+c_0+c_1z^(-1)+c_2z^(-2)+... be an analytic function, regular and univalent for |z|>1, that maps |z|>1 conformally onto the region T preserving the point at ...

A class of area-preserving maps of the form theta_(i+1) = theta_i+2pialpha(r_i) (1) r_(i+1) = r_i, (2) which maps circles into circles but with a twist resulting from the ...

A projection which maps a sphere (or spheroid) onto a plane. Map projections are generally classified into groups according to common properties (cylindrical vs. conical, ...

A plane parallel to two (or more) skew lines, also called a director plane. The orientation of a director is fixed, but it is specified uniquely only if a point lying on it ...

A similarity transformation which preserves orientation, also called a homothety.