Related papers: On mixing diffeomorphisms of the disk

Using pseudoholomorphic curves techniques from symplectic geometry, Barney Bramham proved recently that every smooth irrational pseudo-rotation of the unit disk is the limit, for the $C^0$ topology, of a sequence of smooth periodic…

We prove that every $C^\infty$-smooth, area preserving diffeomorphism of the closed 2-disk having not more than one periodic point is the uniform limit of periodic $C^\infty$-smooth diffeomorphisms. In particular every smooth irrational…

We prove that C^1-robustly transitive diffeomorphisms on surfaces with boundary do not exist, and we exhibit a class of diffeomorphisms of surfaces with boundary which are C^k-robustly transitive, with k greater or equal than 2. This class…

Let $\Sigma$ be a compact surface equipped with an area form. There is an long standing open question by Katok, which, in particular, asks whether every entropy-zero Hamiltonian diffeomorphism of a surface lies in the $C^0$-closure of the…

In this paper we consider closed orientable surfaces $S$ of positive genus and $C^r$-diffeomorphisms $f:S\rightarrow S$ isotopic to the identity ($r\geq 1)$. The main objective is to study periodic open topological disks which are…

The present paper concerns the dynamics of surface diffeomorphisms. Given a diffeomorphism $f$ of a surface $S$, the \emph{torsion} of the orbit of a point $z\in S$ is, roughly speaking, the average speed of rotation of the tangent vectors…

A rational pseudo-rotation $f$ of the torus is a homeomorphism homotopic to the identity with a rotation set consisting of a single vector $v$ of rational coordinates. We give a classification for rational pseudo-rotations with an invariant…

Let $M$ be an $m$-dimensional differentiable manifold with a nontrivial circle action ${\mathcal S}= {\lbrace S_t \rbrace}_{t \in\RR}, S_{t+1}=S_t$, preserving a smooth volume $\mu$. For any Liouville number $\a$ we construct a sequence of…

We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive,…

Asaoka & Irie recently proved a $C^{\infty}$ closing lemma of Hamiltonian diffeomorphisms of closed surfaces. We reformulated their techniques into a more general perturbation lemma for area-preserving diffeomorphism and proved a…

For area preserving $C^2$ surface diffeomorphisms, we give an explicit finite information condition, on the exponential growth of the number of Bowen's $(n,\delta)-$balls needed to cover a positive proportion of the space, that is…

Let M be a smooth compact connected manifold, on which there exists an effective smooth circle action preserving a positive smooth volume. We show that on M, the smooth closure of the smooth volume-preserving conjugation class of some…

The rigidity theory for circle homeomophisms with breaks was studied intensively in the last 20 years. It was proved that under mild conditions of the Diophantine type on the rotation number any two $C^{2+\alpha}$ smooth circle…

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the $C^1$-topology then it…

We study the existence or not of harmonic diffeomorphisms between certain domains in the Euclidean 2-sphere. In particular, we show harmonic diffeomorphisms from circular domains in the complex plane onto finitely punctured spheres, with at…

Let $f:S^1\times [0,1]\to S^1\times [0,1]$ be a real-analytic annulus diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift $\tilde {f}:\mathbb{R}\times [0,1]\rightarrow \mathbb{R}\times…

In this paper we consider $C^{1+\epsilon}$ area-preserving diffeomorphisms of the torus $f,$ either homotopic to the identity or to Dehn twists. We suppose that $f$ has a lift $\widetilde{f}$ to the plane such that its rotation set has…

We prove that the groups of orientation-preserving homeomorphisms and diffeomorphisms of $\mathbb{R}^n$ are boundedly acyclic, in all regularities. This is the first full computation of the bounded cohomology of a transformation group that…

Let $M$ be a closed surface and $f$ a diffeomorphism of $M$. A diffeomorphism is said to permute a dense collection of domains, if the union of the domains are dense and the iterates of any one domain are mutually disjoint. In this note, we…

In this paper, we prove that if an area-preserving non-degenerate diffeomorphism on the open disk which extend smoothly to the boundary with non-degeneracy has at least 2 interior periodic points, then there are infinitely many positive…