Local diffeomorphism information

injective open map. A local diffeomorphism has constant rank of n . {\displaystyle n.} A diffeomorphism is a bijective local diffeomorphism. A smooth covering...

diffeomorphism; those equivalent to a diffeomorphism leaving a simple closed curve invariant; and those equivalent to pseudo-Anosov diffeomorphisms....

Bernoulli map, and Arnold's cat map. If the map is a diffeomorphism, then it is called an Anosov diffeomorphism. If a flow on a manifold splits the tangent bundle...

orientation-preserving diffeomorphism group of M (only the identity component of mappings homotopic to the identity diffeomorphism if you wish) and Diffx1(M)...

Theorem in topology about homeomorphic subsets of Euclidean space Local diffeomorphism Locally Hausdorff space Non-Hausdorff manifold – generalization of...

{\displaystyle \ f\ } is a local diffeomorphism such that   g = f ∗ g ′   , {\displaystyle \ g=f^{*}g'\ ,} then f {\displaystyle f} is called a local isometry. A collection...

following: Theorem — If φ : M → N {\displaystyle \varphi :M\to N} is a local diffeomorphism at x {\displaystyle x} in M {\displaystyle M} , then d φ x : T x...

{G}}} with the same Lie algebroid of G {\displaystyle G} , and a local diffeomorphism G ~ → G {\displaystyle {\tilde {G}}\to G} which is a groupoid morphism...

{\displaystyle {\mathfrak {g}}} . Note that the exponential map is a local diffeomorphism between a neighborhood U of the zero matrix 0 _ ∈ g {\displaystyle...

of all smooth manifolds up to diffeomorphism. Since dimension is an invariant of smooth manifolds up to diffeomorphism type, this classification is often...

In theoretical physics, general covariance, also known as diffeomorphism covariance or general invariance, consists of the invariance of the form of physical...

roughly states that the existence of a local diffeomorphism near a fixed point implies the existence of a local stable center manifold containing that...

Anosov system. Let M be a smooth manifold with a diffeomorphism f: M→M. Then f is an axiom A diffeomorphism if the following two conditions hold: The nonwandering...

regular value, in a neighborhood of each xi the map f is a local diffeomorphism. Diffeomorphisms can be either orientation preserving or orientation reversing...

a Möbius geometry, meaning that there exists an angle preserving local diffeomorphism from the manifold into a Möbius geometry. In two dimensions, every...

of F is an isomorphism at all points p in M then the map F is a local diffeomorphism. The inverse function theorem can also be generalized to differentiable...

injective function is locally injective but not conversely. Local diffeomorphisms, local homeomorphisms, and smooth immersions are all locally injective...

In mathematics, a pseudogroup is a set of diffeomorphisms between open sets of a space, satisfying group-like and sheaf-like properties. It is a generalisation[dubious...

transformation H ( x ) {\displaystyle H(x)} is guaranteed to be a local diffeomorphism. The diagonal matrix M ( x ^ ) {\displaystyle M({\hat {x}})} of gains...

one-dimensional groups of diffeomorphisms) on M, the Lie derivative is the differential of the representation of the diffeomorphism group on tensor fields...

linear mapping of vector bundles. The problem is invariant under local diffeomorphism, so it is sufficient to prove it when M is an open set in Rn and...