Related papers: {\alpha}-limit sets and Lyapunov function for maps…

We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with…

Given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of dimension $p+1$ into a closed Riemannian manifold $\mathcal{N}$. The target manifold is required to satisfy suitable topological conditions; in particular,…

A topology on a nonempty set $X$ specifies a natural subset of $\mathcal{P}(X)$. By identifying $\mathcal{P}(\mathcal{P}(X))$ with the totally disconnected compact Hausdorff space $2^{\mathcal{P}(X)}$, the lattice $Top(X)$ of all topologies…

We explore some properties of Lyapunov exponents of measures preserved by smooth maps of the interval, and study the behaviour of the Lyapunov exponents under topological conjugacy.

This manuscript develops a framework for the strong approximation of Sobolev maps with values in compact manifolds, emphasizing the interplay between local and global topological properties. Building on topological concepts adapted to VMO…

In the present paper we focus on the problem of the existence of strange pseudohyperbolic attractors for three-dimensional diffeomorphisms. Such attractors are genuine strange attractors in that sense that each orbit in the attractor has a…

We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of…

Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…

In this paper, we derive more on $\alpha^{m}$-continuous functions and $\alpha^{m}$-irresolute functions with $\alpha^{m}$-open maps and $\alpha^{m}$-closed maps in topological spaces also we introduce $I_{\alpha^{m}}(A)$ and…

Consider the self-map F of the space of real-valued test functions on the line which takes a test function f to the test function sending a real number x to f(f(x))-f(0). We show that F is discontinuous, although its restriction to the…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

Given an ergodic measure with positive entropy and only positive Lyapunov exponents, its dynamical quantifiers can be approximated by means of quantifiers of some family of uniformly expanding repellers. Here non-uniformly expanding maps…

This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…

We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…

We classify the measure theoretic attractors of general C^3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.

A topological space is locally equiconnected if there exists a neighborhood $U$ of the diagonal in $X\times X$ and a continuous map $\lambda:U\times[0,1]\to X$ such that $\lambda(x,y,0)=x$, $\lambda(x,y,1)=y$ et $\lambda(x,x,t)=x$ for…

Let $M$ be a smooth connected orientable compact surface. Denote by $F(M,S^1)$ the space of all Morse functions $f:M\to S^1$ having no critical points on the boundary of $M$ and such that for every boundary component $V$ of $M$ the…

We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric…

We study piecewise injective, but not necessarily globally injective, contracting maps on a compact subset of \(\bR^d\). We prove that generically the attractor and the set of discontinuities of such a map are disjoint, and hence the…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…