Related papers: Area-preserving diffeomorphisms of the torus whose…

We consider $C^{1+\epsilon}$ diffeomorphisms of the torus, denoted $f,$ homotopic to the identity and whose rotation sets have interior. We give some uniform bounds on the displacement of points in the plane under iterates of a lift of $f,$…

In this paper we consider $C^\infty $-generic families of area-preserving diffeomorphisms of the torus homotopic to the identity and their rotation sets. Let $f_t:\rm{T^2\rightarrow T^2}$ be such a family, $\widetilde{f}_t:\rm…

We construct a $C^\infty$ area-preserving diffeomorphism of the two-dimensional torus which is Bernoulli (in particular, ergodic) with respect to Lebesgue measure, homotopic to the identity, and has a lift to the universal covering whose…

Let $f$ be a $C^{1+\varepsilon}$ diffeomorphism of the closed annulus $A$ that preserves orientation and the boundary components, and $\widetilde{f}$ be a lift of $f$ to its universal covering space. Assume that $A$ is a Birkhoff region of…

We consider closed orientable surfaces $S$ of genus $g>1$ and homeomorphisms $f:S\rightarrow S$ homotopic to the identity. A set of hypotheses is presented, called fully essential system of curves $\mathscr{C}$ and it is shown that under…

In this paper we consider torus homeomorphisms $f$ homotopic to Dehn twists. We prove that if the vertical rotation set of $f$ is reduced to zero, then there exists a compact connected essential "horizontal" set K, invariant under $f$. In…

We consider twist diffeomorphisms of the torus, $f:{\rm T^2\rightarrow T^2,}$ and their vertical rotation intervals $\rho _V(\widehat{f})=[\rho _V^{-},\rho _V^{+}],$ where $\widehat{f}$ is a lift of $f$ to the vertical annulus or cylinder.…

We show that, if $f$ is a homeomorphism of the 2--torus isotopic to the identity, and its lift $\widetilde f$ is transitive, or even if it is transitive outside of the lift of the elliptic islands, then $(0,0)$ is in the interior of the…

Let $f:{\rm T^2\rightarrow T^2}$ be a homeomorphism homotopic to the identity, $\widetilde{f}:{\rm I}\negthinspace {\rm R^2\rightarrow I} \negthinspace {\rm R^2}$ be a fixed lift and $\rho (\widetilde{f})$ be its rotation set, which we…

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…

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…

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…

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…

We consider an area-preserving diffeomorphism of a compact surface, which is assumed to be an irrational rotation near each boundary component. A finite set of periodic orbits of the diffeomorphism gives rise to a braid in the mapping…

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…

We prove that if an area-preserving homeomorphism of the torus in the homotopy class of the identity has a rotation set which is a nondegenerate vertical segment containing the origin, then there exists an essential invariant annulus. In…

We present a dichotomy for surface homeomorphisms in the isotopy class of the identity. We show that, in the absence of a degenerate fixed point set, either there exists a uniform bound on the diameter of orbits of non-wandering points for…

This article deals with nonwandering (e.g. area-preserving) homeomorphisms of the torus $\mathbb{T}^2$ which are homotopic to the identity and strictly toral, in the sense that they exhibit dynamical properties that are not present in…

Let $f$ be a transitive homeomorphism of the two-dimensional torus in the homotopy class of the identity. We show that a lift of $f$ to the universal covering is transitive if and only if the rotation set of the lift contains the origin in…

We consider transitive Anosov diffeomorphisms for which every periodic orbit has only one positive and one negative Lyapunov exponent. We establish various properties of such systems including strong pinching, C^{1+\beta} smoothness of the…