Related papers: Various shadowing properties for time varying maps
For dynamical systems with the shadowing property, we provide a method of approximation of invariant measures by ergodic measures supported on odometers and their almost 1-1 extensions. For a topologically transitive system with the…
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…
In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function…
We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these…
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…
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…
We use symbolic dynamics to study discrete-time dynamical systems with multiple time delays. We exploit the concept of avoiding sets, which arise from specific non-generating partitions of the phase space and restrict the occurrence of…
We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that…
The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow,…
Standard dynamical systems theory is centred around the coordinate-invariant asymptotic-time properties of autonomous systems. We identify three limitations of this approach. Firstly, we discuss how the traditional approach cannot take into…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
Following ideas from a preprint of the second author, see [2], we investigate relations of dynamical Teichmuller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and…
This paper investigates self-maps T from X to X which satisfy a distance constraint in a metric space which mixed point-dependent non-expansive properties, or in particular contractive ones, and potentially expansive properties related to…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
This paper aims at formulating definitions of topological stability, structural stability, and expansiveness property for an iterated function system( abbrev, IFS). It is going to show that the shadowing property is necessary condition for…
We study the dynamical evolution of the deposition interface using both discrete and continuous models for which shadowing effects are important. We explain why continuous and discrete models implying both only shadowing deposition do not…
This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…