Related papers: Exploring F-Sensitivity for Non-Autonomous Systems

We introduce the concept of fidelity for dynamical maps in an open quantum system scenario. We derive an inequality linking this quantity to the distinguishability of the inducing environmental states. Our inequality imposes constraints on…

This paper proves that a set-valued dynamical system is sensitively dependent on initial conditions (resp., $\mathscr{F}$-sensitive, multi-sensitive) if and only if its $g$-fuzzification is sensitively dependent on initial conditions…

Let $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ be a sequence of continuous self-maps on a compact metric space $X$. Firstly, we obtain the relations between topological sequence entropy of a nonautonomous dynamical system $(X,f_{0,\infty})$ and…

In this paper we characterize tame dynamical systems and functions in terms of eventual non-sensitivity and eventual fragmentability. As a notable application we obtain a neat characterization of tame subshifts $X \subset \{0,1\}^{\mathbb…

Sensitivity is a prominent aspect of chaotic behavior of a dynamical system. We study the relevance of nonsensitivity to fixed point theory in affine dynamical systems. We prove a fixed point theorem which extends Ryll-Nardzewski's theorem…

The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…

For a family F (a collection of subsets of Z_+), the notion of F-independence is defined both for topological dynamics (t.d.s.) and measurable dynamics (m.d.s.). It is shown that there is no non-trivial {syndetic}-independent m.d.s.; a…

The deep integration of foundation models (FM) with federated learning (FL) enhances personalization and scalability for diverse downstream tasks, making it crucial in sensitive domains like healthcare. Achieving group fairness has become…

The self-attention mechanism, now central to deep learning architectures such as Transformers, is a modern instance of a more general computational principle: learning and using pairwise affinity matrices to control how information flows…

We consider the system of $N$ points on the segment of the real line with the nearest-neighbor Coulomb repulsive interaction and external force $F$. For the fixed points of such systems (fixed configurations) we study the asymptotics (in…

Given a finite set $X$ and a function $f:X\to X$, we define the degree of noninvertibility of $f$ to be $\displaystyle\text{deg}(f)=\frac{1}{|X|}\sum_{x\in X}|f^{-1}(f(x))|$. This is a natural measure of how far the function $f$ is from…

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…

For a continuous self-map $f$ on a compact interval $I$ and the induced map $\hat f$ on the space $\mathcal{M}(I)$ of probability measures, we obtain a sharp condition to guarantee that $(I,f)$ is transitive if and only if…

In this paper, we study the dimension of planar self-affine sets, of which generating iterated function system (IFS) contains non-invertible affine mappings. We show that under a certain separation condition, the dimension equals to the…

We introduce $(\gamma,\delta)$-similarity, a notion of system comparison that measures to what extent two stable linear dynamical systems behave similarly in an input-output sense. This behavioral similarity is characterized by measuring…

The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…

For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…

Given a nondegenerate compact perfect and Hausdorff topological space $X$,$n\in \mathbb{N}$ and a function $f:X\rightarrow X$, we consider the $n$-fold symmetric product of $X$, $F_n(X)$ and the induced function $F_n(f):F_n(X)\rightarrow…

We consider nonautonomous discrete dynamical systems $\{ f_n\}_{n\ge 1}$, where every $f_n$ is a surjective continuous map $[0,1]\to [0,1]$ such that $f_n$ converges uniformly to a map $f$. We show, among others, that if $f$ is chaotic in…

In this paper notions of strong specification property and quasi-weak specification property for non-autonomous discrete systems are introduced and studied. It is shown that these properties are dynamical properties and are preserved under…