Related papers: A Note on Measure-Expansive Diffeomorphisms

We define the concept of continuum wise expansive for set-valued functions and prove that if a compact metric space admit a set-valued $cw$-expansive function then the topological entropy of $X$ is positive.} We also introduce the notion of…

In this paper we present a new approach to studying g-measures which is based upon local absolute continuity. We extend the result in [11] that square summability of variations of g-functions ensures uniqueness of g-measures. The first…

For a given positive integer $m$, let $A=\set{0,1,...,m}$ and $q \in (m,m+1)$. A sequence $(c_i)=c_1c_2 ...$ consisting of elements in $A$ is called an expansion of $x$ if $\sum_{i=1}^{\infty} c_i q^{-i}=x$. It is known that almost every…

This memoir is concerned with the generic dynamical properties of conservative homeomorphisms of compact manifolds. Several important techniques allowing to prove genericity results are presented: we emphasize the important role played by…

We study expansive dynamical systems in the setting of distributive lattices and their automorphisms, the usual notion of expansiveness for a homeomorphism of a compact metric space being the particular case when the lattice is the topology…

In this article we introduce and study a natural form of expansivity, that we call \textit{metric-independent expansiveness}, for group actions on metrizable spaces. This notion means \textit{expansive with respect to every compatible…

We prove that every $\mathcal{C}^{r}$ diffeomorphism with $r>1$ on a three-dimensional manifold admits symbolic extensions, i.e. topological extensions which are subshifts over a finite alphabet. This answers positively a conjecture of…

Let $\Omega \subset \mbr^2$ be an internal chord-arc domain and $\varphi : \mbs^1 \rightarrow \partial \Omega$ be a homeomorphism. Then there is a diffeomorphic extension $h : \mbd \rightarrow \Omega$ of $\varphi .$ We study the…

The paper introduces a general method to construct conformal measures for a local homeomorphism on a locally compact non-compact Hausdorff space, subject to mild irreducibility-like conditions. Among others the method is used to give…

Let D be a dendrite and f:D-> D a continuous map. Denote by E(D) and B(D) the sets of endpoints and branch points of D respectively. We show that if E(D) is countable (resp. B(D) is discrete) then f is pointwise-recurrent if and only if f…

We show that diffeomorphisms with a dominated splitting of the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular,…

We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…

For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…

We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if the action is expanding in measure. This provides a somewhat…

In this paper, we address the longstanding question of whether expansive homeomorphisms can exist within convex bodies in Euclidean spaces. Utilizing fundamental tools from topology, including the Borsuk-Ulam theorem and Brouwer's…

Combining Kulpa's proof of the cubical Sperner lemma and a dimension theoretic idea of van Mill we give a very short proof of the invariance of dimension, i.e. the statement that cubes [0,1]^n, [0,1]^m are homeomorphic if and only if n=m.…

We study the group of C^{r}-diffeomorphisms of the closed annulus that are isotopic to the identity. We show that, for r different from 3, the linear space of homogeneous quasi-morphisms on this group is one dimensional. Therefore, the…

Given an action of a group $\Gamma$ on a measure space $\Omega$, we provide a sufficient criterion under which two sets $A, B\subseteq \Omega$ are measurably equidecomposable, i.e., $A$ can be partitioned into finitely many measurable…

Periodic surface homemorphisms (diffeomorphisms) play a significant role in the the Nielsen-Thurston classification of surface homeomorphisms. Periodic surface homeomorphisms can be described (up to conjugacy) by using data sets which are…

An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…