Related papers: Dynamical simplices and Fra\"iss\'e theory

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

We study Cantor Staircases in physics that have the Farey-Brocot arrangement for the Q/P rational heights of stability intervals I(Q/P), and such that the length of I(Q/P)is a convex function of 1/P. Circle map staircases and the…

This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen's sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by…

The classic middle-thirds Cantor set leads to a singular continuous measure via a distribution function that is know as the Devil's staircase. The support of the Cantor measure is a set of zero Lebesgue measure. Here, we discuss a class of…

Motivated by results of J. R. Kline and R. L. Moore (1919) that a compact subset of the plane, homeomorphic to a subset of the reals, lies on the arc, we give a purely topological characterisation of compact sets of the reals. This allows…

Using Gottschalk's notion\,---\,weakly locally almost periodic point, we show in this paper that if $f\colon X\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage…

Whether there is similarity between two physical processes in the movement of objects and the complexity of behavior is an essential problem in science. How to seek similarity through the adoption of quantitative and qualitative research…

In this paper we prove that if $f$ is a self-mapping of a nonempty subset $K$ of a normed space $X$ that satisfies some mild conditions, then the minimal displacement of large iterations $f^n$ always dominates that of $f$ along certain…

The Dowker theorem is a classical result in the topology of finite spaces, claiming that any binary relation between two finite spaces defines two homotopy-equivalent complexes (the Dowker complexes). Recently, Barmak strengthened this to a…

Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve Rees construction, allowing to start with…

Let X be an infinite compact metric space with finite covering dimension. Let $\afhpa,\bt: X\to X$ be two minimal homeomorphisms. Suppose that the range of $K_0$-groups of both crossed product C*-algebras s are dense in the space of real…

Let $\Omega\subseteq\mathcal{R}^2$ be a domain, let $X$ be a rearrangement invariant space and let $f\in W^{1}X(\Omega,\mathcal{R}^2)$ be a homeomorphism between $\Omega$ and $f(\Omega)$. Then there exists a sequence of diffeomorphisms…

The main focus of this paper is to explore how much similarity between two dynamical systems. Analogous to the classical Hartman-Grobman theorem, the relationship between two systems can be linked by a homeomorphic map $K$, and the core is…

In this paper we further explore the L-shadowing property defined in [17] for dynamical systems on compact spaces. We prove that structurally stable diffeomorphisms and some pseudo-Anosov diffeomorphisms of the two-dimensional sphere…

An $n$-dimensional ($n\geq 2$) simply connected, compact without boundary Finsler space of positive constant sectional curvature is conformally homeomorphic to an n-sphere in the Euclidean space $\R^{n+1}$.

Let f : X --> X be a dominant rational map of a projective variety defined over a number field. An important geometric-dynamical invariant of f is its (first) dynamical degree d_f= lim SpecRadius((f^n)^*)^{1/n}. For algebraic points P of X…

We show that every homeomorphism between closed measure zero subsets extends to a measure preserving auto-homeomorphism, whenever the Cantor set is endowed with a suitable probability measure. This is valid both for the standard product…

The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of ${\mathbb C}{\mathbb P}^n$ with the minimal possible number of periodic points (equal to $n+1$ by Arnold's conjecture), called here Hamiltonian pseudo-rotations.…

Let $E$ be a linear space and suppose that $A$ is the global attractor of either (i) a homeomorphism $F:E\rightarrow E$ or (ii) a semigroup $S(\cdot)$ on $E$ that is injective on $A$. In both cases $A$ has trivial shape, and the dynamics on…