Related papers: Point transitivity, $\Delta$-transitivity and mult…

For a continuous map f on a compact metric space (X,d), a subset D of X is internally chain transitive if for every x and y in D and every delta > 0 there is a sequence of points {x=x_0,x_1, ...,x_n=y} such that d(f(x_i),x_{i+1}) < delta…

The orbit of a point $x\in X$ in a classical iterated function system (IFS) can be defined as $\{f_u(x)=f_{u_n}\circ\cdots \circ f_{u_1}(x):$ $u=u_1\cdots u_n$ is a word of a full shift $\Sigma$ on finite symbols and $f_{u_i}$ is a…

We study different conditions which turn out to be equivalent to equicontinuity for a transitive compact Hausdorff flow with a general group action. Among them are a notion of "regional" equicontinuity, also known as "Furstenberg"…

The degree of mixing is a fundamental property of a dynamical system. General multi-dimensional shifts cannot be systematically determined. This work introduces constructive and systematic methods for verifying the degree of mixing, from…

Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…

We analyze the sharpness of crossing ("isosbestic") points of a family of curves which are observed in many quantities described by a function f(x,p), where x is a variable (e.g., the frequency) and p a parameter (e.g., the temperature). We…

We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…

Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…

A topological dynamical system $(X,T)$ is called CF-Nil($k$) if it is strictly ergodic and the maximal measurable and maximal topological $k$-step pro-nilfactors coincide as measure preserving systems. Through constructing specific…

We study a minimal lattice model which describes bidirectional transport of "particles" driven along a one dimensional track, as is observed in microtubule based, motor protein driven bidirectional transport of cargo vesicles, lipid bodies…

We give a lower bound for the size of a subset of $\mathbb F_q^n$ containing a rich k-plane in every direction, a k-plane Furstenberg set. The chief novelty of our method is that we use arguments on non-reduced subschemes and flat families…

In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions…

A complete classification of the computational complexity of the fixed-point existence problem for boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes F and graph…

If totally periodic points are dense in a subshift $X$, its automorphism group is residually finite. We show a weak converse: if periodic points are not dense in a subshift $X$, then the automorphism group of $X \times Y$ is not residually…

Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…

We discuss topological equicontinuity and even continuity in dynamical systems. In doing so we provide a classification of topologically transitive dynamical systems in terms of equicontinuity pairs, give a generalisation of the…

For symbolic dynamics with some mild conditions, we solve the lowering topological entropy problem for subsystems and determine the Hausdorff dimension of the level set with given complexity, where the complexity is represented by Hausdorff…

A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact…

In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from…

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…