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

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...

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)...

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...

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

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...

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...

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

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...

more general diffeomorphism group has been the group of choice, which is the infinite dimensional analogue. The high-dimensional diffeomorphism groups used...

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...

whose inverse is also a Lie group homomorphism. Equivalently, it is a diffeomorphism which is also a group homomorphism. Observe that, by the above, a continuous...

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

morphisms (or both) Large diffeomorphism, a diffeomorphism that cannot be continuously connected to the identity diffeomorphism in mathematics and physics...

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...

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...

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

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...

system can be chosen freely under arbitrary diffeomorphisms of spacetime. Both gauge invariance and diffeomorphism invariance reflect a redundancy in the description...

awarded the Wolf Prize in mathematics. Smale proved that the oriented diffeomorphism group of the two-dimensional sphere has the same homotopy type as the...

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 →...

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...

spatial diffeomorphism on γ {\displaystyle \gamma } instead. Therefore, the meaning of O ^ ′ {\displaystyle {\hat {O}}'} is a spatial diffeomorphism on γ...

structure of phase space, and is called a canonical transformation. A diffeomorphism between two symplectic manifolds f : ( M , ω ) → ( N , ω ′ ) {\displaystyle...

constraint technically refers to a linear combination of spatial and time diffeomorphism constraints reflecting the reparametrizability of the theory under both...

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

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