Related papers: Nowhere dense competing holes in open dynamical sy…

This article consists in applications of [arXiv:2511.14232] in the case of homemomorphisms of higher genus surfaces whose homological rotation set is big enough -- a class of dynamics that is open. We first prove a structure theorem for the…

Let $M$ be a compact orientable surface equipped with a volume form $\omega$, $P$ be either $\mathbb{R}$ or $S^1$, $f:M\to P$ be a $C^{\infty}$ Morse map, and $H$ be the Hamiltonian vector field of $f$ with respect to $\omega$. Let also…

One main task of smooth dynamical systems consists in finding a good decomposition into elementary pieces of the dynamics. This paper contributes to the study of chain-recurrence classes. It is known that $C^1$-generically, each…

We introduce and study a new topological notion of the size for subsets of the real line, called \emph{super-density}. A set $A\subset\mathbb{R}$ is super-dense if for every non-empty open interval $I$ and every nowhere constant continuous…

Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…

Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory,…

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…

Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…

We construct a continuum of non-homeomorphic compact subspaces of the real line R without singleton components. Thus from the purely topological point of view the real line contains not only more closed sets than open sets but also more…

For every $r\in\mathbb{N}_{\geq 2}\cup\{\infty\}$, we prove a $C^r$-orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with 1-dimensional orientation preserving center bundle. To be…

We study expansive dynamical systems from the viewpoint of general topology. We introduce the notions of orbit and refinement expansivity on topological spaces extending expansivity in the compact metric setting. Examples are given on…

This article is devoted to the study of a $2$-dimensional piecewise smooth (but possibly) discontinuous dynamical system, subject to a non-autonomous perturbation; we assume that the unperturbed system admits a homoclinic trajectory…

Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \Vert f(z) \Vert=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…

Let $\Omega\subset\mathbb{R}^n$ be an open set and let $f\in W^{1,p}(\Omega,\mathbb{R}^n)$ be a weak (sequential) limit of Sobolev homeomorphisms. Then $f$ is injective almost everywhere for $p>n-1$ both in the image and in the domain. For…

Suppose M is a noncompact connected n-manifold and m is a good Radon measure of M with m(bdry M) = 0. Let H(M; m) denote the group of m-preserving homeomorphisms of M equipped with the compact-open topology and H_E(M; m) denote the subgroup…

We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, a…

Let $X$ be a compact metric space which is locally absolutely retract and let $\phi: C(X)\to C(Y, M_n)$ be a unital homomorphism, where $Y$ is a compact metric space with ${\rm dim}Y\le 2.$ It is proved that there exists a sequence of $n$…

Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \| f(z) \|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…

Let $n\geq 3$ and let $\Omega \subset \mathbb{R}^n$ be a $\mathcal{C}^1$ bounded domain which is diffeomorphic to a ball. We investigate here the problem of finding critical points of the $n$-energy in the space $\mathcal{I}=\{v\in…

This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…