Related papers: Interval maps with dense periodicity

Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ a continuous function. We consider the set of points for which the Birkhoff average of $\varphi$ does…

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…

Consider a plane graph G, drawn with straight lines. For every pair a,b of vertices of G, we compare the shortest-path distance between a and b in G (with Euclidean edge lengths) to their actual distance in the plane. The worst-case ratio…

In this article, we prove the existence of common fixed points for a pair of maps on a $q$-spherically complete $T_0$-ultra-quasi-metric space. The present article is a generalization, in the assymmetric setting of the paper of Rao et…

In this paper, we study the topological properties and the gap sequences of Bedford-McMullen sets. First, we introduce a topological condition, the component separation condition (CSC), and a geometric condition, the exponential rate…

Recent studies in ecology and epidemiology indicate that it is important to include spatial heterogeneity, synchronization and seasonality in the theoretical models. In this work, spatial heterogeneity is introduced via coupled map lattices…

Trustworthy decision making in networked, dynamic environments calls for innovative uncertainty quantification substrates in predictive models for graph time series. Existing conformal prediction (CP) methods have been applied separately to…

In this paper, we introduce dynamic coprime labeling (DCL), a novel extension of coprime labeling for time-sensitive networks. In particular, we explore whether there exists a graph labeling scheme that maintains relative coprimality among…

We generalize the definition of topological entropy due to Adler, Konheim, and McAndrew \cite{AKM} to set-valued functions from a closed subset $A$ of the interval to closed subsets of the interval. We view these set-valued functions, via…

We study a certain class circle maps which are constant on one interval (called flat piece), and such that the degrees of the singularities at the boundary of the flat piece are different. In this paper, we show that if the topological…

We prove that local stable/unstable sets of homeomorphisms of an infinite compact metric space satisfying the gluing-orbit property always contain compact and perfect subsets of the space. As a consequence, we prove that if a positively…

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of…

We present recent advances in formal verification and control for autonomous systems with practical safety guarantees enabled by conformal prediction (CP), a statistical tool for uncertainty quantification. This survey is particularly…

In this paper, we introduce novel variations on several well-known model-theoretic tree properties, and prove several equivalences to known properties. Motivated by the study of generalized indiscernibles, we introduce the notion of the…

There are lots of results to study dynamical complexity on irregular sets and level sets of ergodic average from the perspective of density in base space, Hausdorff dimension, Lebesgue positive measure, positive or full topological entropy…

We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive…

We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of…

For every $r\in\mathbb{N}_{\geq2}\cup\{\infty\}$, we prove the $C^r$-closing lemma for general and conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle. In particular, it implies periodic points are dense for…

The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as Cross-Correlation (CC) and Mutual Information…

Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. The Temporal $\Delta$ Clique problem, that generalizes the well known Clique problem to temporal graphs, has…