Diffeomorphisms

feature of a system that is preserved under some transformation

In mathematics, a diffeomorphism is an isomorphism of differentiable manifolds. It is an invertible function that maps one differentiable manifold to another such that both the function and its inverse are continuously differentiable.

theoretical physics principle

class of chaotic maps of the square into itself

right|thumb|The complex exponential function mapping biholomorphically a rectangle to a quarter-annulus. In the mathematical theory of functions of one or more complex variables, and also in complex algebraic geometry, a biholomorphism or biholomorphic function is a bijective holomorphic function whose inverse is also holomorphic.

problem in geometric topology

diffeomorphism that has a hyperbolic structure on the tangent bundle

a class of dynamical systems