Related papers: N-expansive homeomorphisms on surfaces

In this paper we study the polynomial entropy of homeomorphism on compact metric space. We construct a homeomorphism on a compact metric space with vanishing polynomial entropy that it is not equicontinuous. Also we give examples with…

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $ M^2_ \mathcal B$ is a supporting surface for $ \mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is…

Let $f\colon M\to M$ be an expansive homeomorphism with dense topologically hyperbolic periodic points, $M$ a compact manifold. Then there is a local product structure in an open and dense subset of $M$. Moreover, if some topologically…

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…

We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…

We prove that if f is an orientation-preserving homeomorphism of a closed orientable surface M whose singular set is totally disconnected, then f is topologically conjugate to a conformal transformation.

We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the…

This paper studies homeomorphisms of surfaces isotopic to the identity by means of purely topological methods and Brouwer theory. The main development is a novel theory of orbit forcing using maximal isotopies and transverse foliations.…

Let $X$ be a compact metric space and let $f:X\rightarrow X$ be a homeomorphism on $X$. We show that if $f$ is both pointwise recurrent and expansive, then the dynamical system $(X, f)$ is topologically conjugate to a subshift of some…

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive…

Let X and Y be compact, simply connected and locally connected subsets of R^2, and let f : X -> Y be a homeomorphism isotopic to the identity on X. Generalizing Brouwer's plane translation theorem for self-maps of the plane, we prove that f…

The existence of quasimorphisms on groups of homeomorphisms of manifolds has been extensively studied under various regularity conditions, such as smooth, volume-preserving, and symplectic. However, in this context, nothing is known about…

This article deals with directional rotational deviations for non-wandering periodic point free homeomorphisms of the 2-torus which are homotopic to the identity. We prove that under mild assumptions, such a homeomorphism exhibits uniformly…

On closed symplectically aspherical manifolds, Schwarz proved a classical result that the action function of a nontrivial Hamiltonian diffeomorphism is not constant by using Floer homology. In this article, we generalize Schwarz's theorem…

In this work we develop a new criterion for the existence of topological horseshoes for surface homeomorphisms in the isotopy class of the identity. Based on our previous work on forcing theory, this new criterion is purely topological and…

In this paper, we study rigidity problems between Lyapunov exponents along periodic orbits and geometric structures. More specifically, we prove that for a surface M without focal points, if the value of the Lyapunov exponents is constant…

A local description of the non-flat infinitesimally bendable Euclidean hypersurfaces was recently given by Dajczer and Vlachos \cite{DaVl}. From their classification, it follows that there is an abundance of infinitesimally bendable…

In this article we consider homeomorphisms of the open annulus $\mathbb{A}=\mathbb{R}/\mathbb{Z}\times \mathbb{R}$ which are isotopic to the identity and preserve a Borel probability measure of full support, focusing on the existence of…

We will construct surfaces of revolution with finite total curvature whose Gauss curvatures are not bounded. Such a surface of revolution is employed as a reference surface of comparison theorems in radial curvature geometry. Moreover, we…

We give an example of a smooth characteristic embedding of a torus in $\s^2 \times \s^2 \# \s^1 \times \s^3$ such that there exists no diffeomorphism of the ambient $4$-manifold that induces the Dehn twist along a meridian of the torus, but…