We recall that two Riemannian manifolds (M,g) and (M',g') are equivalent if there exists a diffeomorphism
([phi]): M [right arrow] M' such that
We now define the so-called Lie derivative which can be used to define a diffeomorphism
invariant in [C.
System (1) is said to be static state feedback linearizable if there exist a state diffeomorphism
An important special case is furnished by the Jacobian determinant L = J(x)(t) associated to a diffeomorphism
The terms in the round brackets are just the components of our Lie derivative which can be used to define a diffeomorphism
The mapping [GAMMA] is a diffeomorphism
which reduces to the identity on the frontier F of U.
This equation  is also similar to the one proposed by Doebner and Goldin  from considerations of unitary representations of the diffeomorphism
Large Deformation Diffeomorphism
and Momentum Based Hippocampal Shape Discrimination in Dementia of the Alzheimer type.
[psi]: X [right arrow] X, defined by
the concircular geometry, is generalization of inversive geometry in the sense that the change of metric is more general than that induced by a circle preserving diffeomorphism
This approach does not take into account the constraint that one seeks a one-to-one warping, which is called a diffeomorphism
The coordinate transformation [mu] is a global diffeomorphism
, analogous to a similarity transformation in linear systems.