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{{short description|On the connectivity of a group of diffeomorphisms of a manifold}} ...n Cerf]]'s which refers to the connectivity of a group of [[Diffeomorphism|diffeomorphisms]] of a manifold. ...

...<math>\varphi : \R^n \to \R^n</math> and <math>\psi : \R \to \R</math> be diffeomorphisms and <math>f: \R^n \to \R</math> any smooth function. We define the group ac ...

Another equivalent statement is that the group of diffeomorphisms of the [[Ball (mathematics)|3-ball]] which restrict to the identity on the ...imself.<ref>{{Cite journal|last=Smale|first=Stephen|date=August 1959|title=Diffeomorphisms of the 2-Sphere|journal=Proceedings of the American Mathematical Society|vo ...

...hi^k(x) = x </math>. A feature of Hamiltonian dynamics is that Hamiltonian diffeomorphisms tend to have infinitely many periodic points. [[Conley]] first made such a ...=http://eudml.org/doc/123400 |title=Periodic points of Hamiltonian surface diffeomorphisms |journal=Geometry & Topology |date=2003 |volume=7 |pages=713–756 |last1=Fra ...

...|central extension]] of the [[Diffeomorphism#Diffeomorphism group|group of diffeomorphisms]] of the [[circle]]. The corresponding [[Lie algebra]] is the [[Virasoro al ...is group is the [[universal cover]] of the group of orientation-preserving diffeomorphisms of the circle, denoted as <math>\widetilde{\text{Diff}}{}^+(S^1)</math>. ...

...the [[Sheaf (mathematics)|sheaf]] of [[germ (mathematics)|germ]]s of local diffeomorphisms of <math>\R^q</math> satisfy the 1-cocycle condition ...s Haefliger structures are defined by replacing sheaves of germs of smooth diffeomorphisms by the appropriate sheaves. ...

...s a manifold with an action of a [[topological group]] ''G'' by analytical diffeomorphisms, the notion of a '''(''G'', ''X'')-structure''' on a [[topological space]] ...s definition is inspired by the analytic continuation property of analytic diffeomorphisms on an [[analytic manifold]]). ...

...l_\lambda</math> on <math>X</math>, whose flow is a one-parameter group of diffeomorphisms of <math>X</math>. Conversely, let <math>\tau=\tau^\lambda\partial_\lambda< ..., one considers a monomorphism <math>f\to\widetilde f</math> of a group of diffeomorphisms of <math>X</math> to a group of bundle automorphisms of a natural bundle <m ...

...meomorphism]] of ''S''.<ref>W. Thurston, ''On the geometry and dynamics of diffeomorphisms of surfaces'', [[Bulletin of the American Mathematical Society]], vol. 19 ( ...

...diffeomorphisms|title=Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms|series=Lecture Notes in Mathematics| date=2008|volume=470|pages=63–76|publi ...

...orbit <math> m \in \mathcal{M} </math> under the action from the group of diffeomorphisms. ==The diffeomorphisms group generated as Lagrangian and Eulerian flows== ...

==Operator representation of points, vector fields and diffeomorphisms== * '''Diffeomorphisms''' <math>P:M\to M</math> are identified with <math>C^\infty(M)</math>-autom ...

...th>, then there exists a family <math>\{ \psi_t \}_{t \in [0,1]}</math> of diffeomorphisms of <math>M</math> such that <math>\psi_t^*\omega_t = \omega_0</math> and <m One implication holds by the invariance of the integral by diffeomorphisms: <math>\int_M \alpha_0 = \int_M \psi^*\alpha_1 = \int_{\psi(M)} \alpha_1 = ...

=== Pseudo-Anosov diffeomorphisms === ...

...math>. The family of vector fields integrates to a 1-parameter family of [[diffeomorphisms]] <math>\varphi_t: M \to M</math>. Each individual <math>\varphi_t</math> i ...onal of <math>M\times M</math> transversely. For nondegenerate Hamiltonian diffeomorphisms, one variant of the Arnold conjecture says that the number of fixed points ...

...39284|last1=Bedford|first1=Eric|last2=Smillie|first2=John|title=Polynomial Diffeomorphisms of C². II: Stable Manifolds and Recurrence|journal=Journal of th *{{cite journal|arxiv=math/9205210|doi=10.1007/BF01232426|title=Polynomial diffeomorphisms of <math>C^2</math>. IV: The measure of maximal entropy and laminar current ...

...ooth <math>n</math>-dimensional manifolds and [[Local diffeomorphism|local diffeomorphisms]]. Consider also the category <math>\mathcal{FM}</math> of [[Fibered manifo ...epends only on the jet <math>j^r_x f</math>. Equivalently, for every local diffeomorphisms <math>f,g: M \to N</math> and every point <math>x \in M</math>, one has<mat ...

* Bowen: "Markov partitions for Axiom A diffeomorphisms", ''[[American Journal of Mathematics]]'', vol. 92 (1970), pp.&nbsp;725–747 * Bowen: "Periodic points and measures for Axiom A diffeomorphisms", ''[[Transactions of the American Mathematical Society]]'', 1971, pp.&nbsp ...

...le. In the CGHS model, if we include [[Faddeev–Popov ghost]]s to gauge-fix diffeomorphisms in the [[conformal gauge]], they contribute an anomaly of -24. Each matter ...