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...

U → f ( U ) {\displaystyle f\vert _{U}:U\to f(U)} is a diffeomorphism. A local diffeomorphism is a special case of an immersion f : X → Y {\displaystyle...

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

theoretical physics, a large diffeomorphism is an equivalence class of diffeomorphisms under the equivalence relation where diffeomorphisms that can be continuously...

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...

theoretical physics, it is often important to study theories with the diffeomorphism symmetry such as general relativity. These theories are invariant under...

synonymous with diffeomorphism anomaly, since general covariance is symmetry under coordinate reparametrization; i.e. diffeomorphism. General covariance...

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...

pseudo-Anosov map is a type of a diffeomorphism or homeomorphism of a surface. It is a generalization of a linear Anosov diffeomorphism of the torus. Its definition...

group elements are diffeomorphisms. The structure of a G-space is a group homomorphism ρ : G → Diffeo(X) into the diffeomorphism group of X. Riemannian...

differ by a diffeomorphism of the unit circle. On the other hand, a diffeomorphism f of the unit circle can be extended to a diffeomorphism F of the unit...

a Hamiltonian function H). A Hamiltonian diffeomorphism of a symplectic manifold (M, ω) is a diffeomorphism Φ of M which is the integral of a smooth path...

G\times _{G_{x}}T_{x}M/T_{x}(G\cdot x)} so that it defines an equivariant diffeomorphism from the neighborhood to its image, which contains the orbit of x {\displaystyle...

imaging. The study of deformable shapes in CA rely on high-dimensional diffeomorphism groups Diff V {\displaystyle \operatorname {Diff} _{V}} which generate...

the entire manifold M is hyperbolic, the map f is called an Anosov diffeomorphism. The dynamics of f on a hyperbolic set, or hyperbolic dynamics, exhibits...

In mathematics, Denjoy's theorem may refer to several theorems proved by Arnaud Denjoy, including Denjoy–Carleman theorem Denjoy–Koksma inequality Denjoy–Luzin...

Smale conjecture, named after Stephen Smale, is the statement that the diffeomorphism group of the 3-sphere has the homotopy-type of its isometry group, the...

interpreted as a continuous 1-cocycle or crossed homomorphism of the diffeomorphism group of the circle with coefficients in the module of densities of...

up to a diffeomorphism. For example, if M and N are two Riemannian manifolds with metrics g and h, respectively, when is there a diffeomorphism ϕ : M →...

gives a sufficient condition for a diffeomorphism of the circle to be topologically conjugate to a diffeomorphism of a special kind, namely an irrational...

transformations homeomorphisms and diffeomorphisms since they carry smooth submanifolds smoothly during transformation. Diffeomorphisms are generated in the modern...

ϕ {\displaystyle \phi } . When the map ϕ {\displaystyle \phi } is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform...

to a diffeomorphism, the extension cannot always be done in the plane. For example, the map on the right needs to be extended to a diffeomorphism of the...

commutation relations with the diffeomorphism constraints generate the Bergman–Komar "group" (which is the diffeomorphism group on-shell). In canonical...

spaces. A homeomorphism is an isomorphism of topological spaces. A diffeomorphism is an isomorphism of spaces equipped with a differential structure,...

states: Let f be a diffeomorphism of a compact manifold with a nonwandering point x. Then, there is (in the space of diffeomorphisms, equipped with the...

structures on the 7-sphere. In any dimension Milnor (1959) showed that the diffeomorphism classes of oriented exotic spheres form the non-trivial elements of...

The first class constraints of general relativity are the spatial diffeomorphism constraint and the Hamiltonian constraint (also known as the Wheeler–De...