Related papers: Pointwise-recurrent dendrite maps

Let $X$ be a compact metric countable space, let $f:X\to X$ be a homeomorphism and let $E(X,f)$ be its Ellis semigroup. Among other results we show that the following statements are equivalent: (i) $(X,f)$ is equicontinuous, (ii) $(X,f)$ is…

We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a…

The goal of the article is to characterize the conservative homeomorphisms of a closed orientable surface $S$ of genus $\geq 2$, that have finitely many periodic points. By conservative, we mean a map with no wandering point. As a…

Given a dendrite $X$ and a continuous map $f\colon X\to X$, we show the following are equivalent: (i) $\omega_f$ is continuous and $\overline{\mathrm{Per}(f)}=\bigcap_{n\in\mathbb{N}}f^n(X)$; (ii) $\omega(x,f)=\Omega(x,f)$ for each $x\in…

We study the problem of existence of a periodic point in the boundary of an invariant domain for a surface homeomorphism. In the area-preserving setting, a complete classification is given in terms of rationality of Carath\'eordory's prime…

A group $\Gamma$ is said to be periodic if for any $g$ in $\Gamma$ there is a positive integer $n$ with $g^n=id$. We first prove that a finitely generated periodic group acting on the 2-sphere $\SS^2$ by $C^1$-diffeomorphisms with a finite…

We prove that every Peano continuum (a space that is a continuous image of $[0,1]$) admits a topologically mixing but not exact map. The constructed map has a dense set of periodic points.

This work dynamically classifies a 9-parametric family of birational maps f : C2 -> C2. From the sequence of the degrees dn of the iterates of f, we find the dynamical degree delta(f) of f. We identify when dn grows periodically, linearly,…

We show that $C(X)$ admits an equivalent pointwise lower semicontinuous locally uniformly rotund norm provided $X$ is Fedorchuk compact of spectral height 3. In other words $X$ admits a fully closed map $f$ onto a metric compact $Y$ such…

We prove that a subshift $(X,T)$ is linearly recurrent if and only if it is a primitive and proper $S$-adic subshift. This corrects Proposition 6 in F. Durand ({\it Ergod. Th. & Dynam. Sys. {\bf 20}} (2000), 1061--1078).

Let f be a class P -homeomorphism of the circle. We prove that there exists a piecewise analytic homeomorphism that conjugate f to a one-class P with prescribed break points lying on pairwise distinct orbits. As a consequence, we give a…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

Let $ R $ be a rational map with totally disconnected Julia set $ J(R). $ If the postcritical set on $ J(R) $ contains a non-persistently recurrent (or conical) point, then we show that the map $ R $ can not be a structurally stable map.

In this paper, we study the periodic and eventually periodic points of affine infra-nilmanifold endomorphisms. On the one hand, we give a sufficient condition for a point of the infra-nilmanifold to be (eventually) periodic. In this way we…

It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. Considering the Foata normal form metric on trace monoids and uniformly continuous endomorphisms, a…

In the present note we focus on dynamics on the Gehman dendrite $\mathcal{G}$. It is well-known that the set of its endpoints is homeomorphic to a standard Cantor ternary set. For any given surjective Cantor system $\mathcal{C}$ we provide…

In this follow-up paper, we again inspect a surprising relationship between the set of $m$-periodic points of a polynomial map $\varphi_{d, c}$ defined by $\varphi_{d, c}(z) = z^d + c$ for all $c, z \in \mathcal{O}_{K}$ and the coefficient…

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…

Let $V$ be a quasiprojective variety defined over $\mathbb{F}_q$, and let $\phi:V\rightarrow V$ be an endomorphism of $V$ that is also defined over $\mathbb{F}_q$. Let $G$ be a finite subgroup of $\operatorname{Aut}_{\mathbb{F}_q}(V)$ with…

We prove that if a homeomorphism of a closed orientable surface S has no wandering points and leaves invariant a compact, connected set K which contains no periodic points, then either K=S and S is a torus, or $K$ is the intersection of a…