Related papers: Transitive dendrite map with zero entropy
We study the existence of Riemannian metrics with zero topological entropy on a closed manifold M with infinite fundamental group. We show that such a metric does not exist if there is a finite simply connected CW complex which maps to M in…
We prove that every topologically transitive shift of finite type in one dimension is topologically conjugate to a subshift arising from a primitive random substitution on a finite alphabet. As a result, we show that the set of values of…
The aim of this work is to exhibit an example of an endomorphism of $\T^{2}$ which is $C^2$-robustly transitive but not $C^1$-robustly transitive.
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
We study metric versions of transitivity, mixing, and hypercyclicity for continuous maps, based on intersections of the form \( f^{n}(U)\cap B_{\delta}(V)\neq\varnothing. \) We introduce $\delta$-topological transitivity,…
We explore the dynamics of graph maps with zero topological entropy. It is shown that a continuous map $f$ on a topological graph $G$ has zero topological entropy if and only if it is locally mean equicontinuous, that is the dynamics on…
It is known that piecewise affine surface homeomorphisms always have measures of maximal entropy. This is easily seen to fail in the discontinuous case. Here we describe a piecewise affine, globally continuous surface map with no measure of…
We construct a $C^r$ transformation of the interval (or the torus) which is topologically mixing but has no invariant measure of maximal entropy. Whereas the assumption of $C^{\infty}$ ensures existence of maximal measures for an interval…
It is shown that if a non-invertible area preserving local homeomorphism on $\mathbb{T}^2$ is homotopic to a linear expanding or hyperbolic endomorphism, then it must be topologically transitive. This gives a complete characterization, in…
The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we…
Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field…
In a previous paper ("A characterization of topologically completely positive entropy for shifts of finite type"), the author gave a characterization for when a $\mathbb{Z}^d$-shift of finite type (SFT) has no nontrivial subshift factors…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
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.
The topological entropy of a continuous self-map of a compact metric space can be defined in several distinct ways; when the space is not assumed compact, these definitions can lead to distinct invariants. The original, purely topological…
For $Y \subset X$ a locally complete intersection of codimension p, Spencer Bloch [2] constructed the semi-regularity map $\pi: H^{1}(\mathcal{N}_{Y/X}) \to H^{p+1}(\Omega_{X/k}^{p-1})$. As an analogue, we construct a map $\tilde{\pi}:…
We study the topological entropy of hom tree-shifts and show that, although the topological entropy is not a conjugacy invariant for tree-shifts in general, it remains invariant for hom tree higher block shifts. In…
This paper is concerned with some stronger forms of transitivity in non-autonomous discrete systems$(f_{ 1,\infty})$ generated by a uniformly convergent sequence of continuous self maps. Firstly, we present two counterexamples to show that…
Quasi-vertex-transitive maps are the homogeneous maps on the plane with finitely many vertex orbits under the action of their automorphism groups. We show that there exist quasi-vertex-transitive maps of types $[p^3, 3]$ for $p \equiv 1$…
Given a tree map $f:T\to T$, we study the dynamics of subcontinua of $T$ under action of $f$. In particular, we prove that a subcontinuum of $T$ is either asymptotically periodic or asymptotically degenerate. As an application of this…