Related papers: Rotation sets with nonempty interior and transitiv…

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…

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…

In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that…

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…

We prove that for a torus homeomorphism isotopic to the identity and with a lift whose rotation set is an interval, either every rational point in the rotation set is realized by a periodic orbit, or there exists an annular, essential,…

Let $K_1$, $K_2$ $\subset$ $R^2$ be two convex, compact sets. We would like to know if there are commuting torus homeomorphisms $f$ and $h$ homotopic to the identity, with lifts $\tilde f$ and $\tilde h$, such that $K_1$ and $K_2$ are their…

In this paper, we study non-wandering homeomorphisms of the two torus in the identity homotopy class, whose rotation sets are non-trivial line segments from $(0,0)$ to some totally irrational vector $(\alpha,\beta)$. We show this rotation…

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…

A homeomorphism f of a manifold M is called H_1-transitive if there is a transitive lift of an iterate of f to the universal Abelian cover \tM. Roughly speaking, this means that f has orbits which repeatedly and densely explore all elements…

We study homotopic-to-the-identity torus homeomorphisms, whose rotation set has nonempty interior. We prove that any such map is monotonically semiconjugate to a homeomorphism that preserves the Lebesgue measure, and that has the same…

We prove that a homeomorphism of the torus homotopic to the identity whose rotation set is reduced to a single totally irrational vector is chain-recurrent. In fact, we show that pseudo-orbits can be chosen with a small number of jumps, in…

It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, 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…

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 $C^{1+\epsilon}$ 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…

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…

Let $C(\mathbf I)$ be the set of all continuous self-maps from ${\mathbf I}=[0,1]$ with the topology of uniformly convergence. A map $f\in C({\mathbf I})$ is called a transitive map if for every pair of non-empty open sets $U,V$ in…

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…

We consider the rotation set $\rho(F)$ for a lift $F$ of an area preserving homeomorphism $f: \t^2\to \t^2$, which is homotopic to the identity. The relationship between this set and the existence of periodic points for $f$ is least well…

Let $f$ be a homeomorphism of the closed annulus $A$ that preserves orientation, boundary components and that has a lift $\tilde f$ to the infinite strip $\tilde A$ which is transitive. We show that, if the rotation number of both boundary…