Related papers: On almost specification and average shadowing prop…

An intuitively necessary requirement of models used to provide forecasts of a system's future is the existence of shadowing trajectories that are consistent with past observations of the system: given a system-model pair, do model…

We characterize and describe the extensions of expansive and Anosov homeomorphisms on compact spaces. As an application we obtain a stability result for extensions of Anosov systems, and show a construction that embeds any expansive system…

This article provides the second part of the research initiated in arXiv:2411.17381, where we introduced and investigated so called periodicity shadows, which are special skew-symmetric matrices related to symmetric algebras with periodic…

In this work, we propose a new existence result for quasi-equilibrium problems using generalized monotonicity in an infinite dimensional space. Also, we show that the notions of generalized monotonicity can be characterized in terms of…

In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…

We use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism. A new concept of shadowing in which we control…

We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…

Metric of axially symmetric asymptotically flat black holes in an arbitrary metric theory of gravity can be represented in the general form which depends on infinite number of parameters. We constrain this general class of metrics by…

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…

We study dynamical systems $(X,G,m)$ with a compact metric space $X$ and a locally compact, $\sigma$-compact, abelian group $G$. We show that such a system has discrete spectrum if and only if a certain space average over the metric is a…

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

We consider contractive systems whose trajectories evolve on a compact and convex state-space. It is well-known that if the time-varying vector field of the system is periodic then the system admits a unique globally asymptotically stable…

We introduce pointwise measure expansivity for bi-measurable maps. We show through examples that this notion is weaker than measure expansivity. In spite of this fact, we show that many results for measure expansive systems hold true for…

One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact…

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…

Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to…

In this paper, we employ a ray-tracing algorithm to simulate the shadows of three equal-mass black holes in static equilibrium across a wide parameter space. We find that the shadows consist of a larger primary shadow and several distorted,…

Using techniques of non-autonomous dynamical systems, we completely characterize the persistence properties of an almost periodic Nicholson system in terms of some numerically computable exponents. Although similar results hold for a class…

We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…

We prove a compactness criterion for asymptotic $L_p$ spaces over arbitrary measure spaces. Total boundedness is characterized by almost equiboundedness together with total boundedness in $L_p$ of all truncations. This gives a…