Related papers: Lowering topological entropy over subsets revisite…

We consider a two-parameter family of random substitutions and show certain combinatorial and topological properties they satisfy. We establish that they admit recognisable words at every level. As a consequence, we get that the subshifts…

A toroidal set is a compactum $K \subseteq \mathbb{R}^3$ which has a neighbourhood basis of solid tori. We study the topological entropy of toroidal attractors $K$, bounding it from below in terms of purely topological properties of $K$. In…

Strong regulations in the financial industry mean that any decisions based on machine learning need to be explained. This precludes the use of powerful supervised techniques such as neural networks. In this study we propose a new…

We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/\alpha}$ with the size of the…

We show that for every topological dynamical system with the approximate product property, zero topological entropy is equivalent to unique ergodicity. Equivalence of minimality is also proved under a slightly stronger condition. Moreover,…

Let (M,J) be a dynamical model of macroscopic systems and (N,K) a less microscopic model (i.e. a model involving less details) of the same macroscopic systems; M and N are manifolds, J are vector fields on M, and K are vector fields on N.…

Suppose f is a C^{1+\epsilon} surface diffeomorphism with positive topological entropy. For every positive \delta strictly smaller than the topological entropy of f we construct an invariant Borel set E such that (a) f|E has a countable…

We consider a tippe top modeled as an eccentric sphere, spinning on a horizontal table and subject to a sliding friction. Ignoring translational effects, we show that the system is reducible using a Routhian reduction technique. The reduced…

Let $(X,T)$ be a topological dynamical system and $n\geq 2$. We say that $(X,T)$ is $n$-tuplewise IP-sensitive (resp. $n$-tuplewise thickly sensitive) if there exists a constant $\delta>0$ with the property that for each non-empty open…

Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…

This paper deals with the topological entropy for hom Markov shifts $\mathcal{T}_M$ on $d$-tree. If $M$ is a reducible adjacency matrix with $q$ irreducible components $M_1, \cdots, M_q$, we show that $h(\mathcal{T}_{M})=\max_{1\leq i\leq…

Given a dynamical system $(X,G)$, the centralizer $C(G)$ denotes the group of all homeomorphisms of $X$ which commute with the action of $G$. This group is sometimes called the automorphism group of the dynamical system $(X,G)$. In this…

A $k$-graph system $\textbf{H}=\{H_i\}_{i\in[m]}$ is a family of not necessarily distinct $k$-graphs on the same $n$-vertex set $V$ and a $k$-graph $H$ on $V$ is said to be $\textbf{H}$-transversal provided that there exists an injection…

We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…

This article is devoted to study which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive.…

In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy class. The topological entropy of this graph representative…

We prove that every self-homeomorphism $h : K_s \to K_s$ on the inverse limit space $K_s$ of the tent map $T_s$ with slope $s \in (\sqrt 2, 2]$ has topological entropy $\htop(h) = |R| \log s$, where $R \in \Z$ is such that $h$ and…

Let f be an orientation-preserving homeomorphism of the disk D, P a finite invariant subset and [f] the isotopy class of f in D\P. We give a non trivial lower bound of the topological entropy for maps in [f], using the spectral radius of…

Let S be a compact, connected surface and H in C^2(T^* S) a Tonelli Hamiltonian. This note extends V. V. Kozlov's result on the Euler characteristic of S when H is real-analytically integrable, using a definition of topologically-tame…

The theoretical and numerical understanding of the key concept of topological entropy is an important problem in dynamical systems. Most studies have been carried out on maps (discrete-time systems). We analyse a scenario of global changes…