Related papers: Various shadowing properties for time varying maps
We develop spectral theorems for nonautonomous linear difference systems, considering different types of $\mu$-dichotomies, both uniform and nonuniform. In the nonuniform case, intriguing scenarios emerge -- that have been employed but…
For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.
In this article we show that there are homeomorphisms of plane continua whose conjugacy class is residual and have the shadowing property.
In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
In the last decades, complex networks theory significantly influenced other disciplines on the modeling of both static and dynamic aspects of systems observed in nature. This work aims to investigate the effects of networks' topological…
We prove that, under a mild condition on the hyperbolicity of its periodic points, a map $g$ which is topologically conjugated to a hyperbolic map (respectively, an expanding map) is also a hyperbolic map (respectively, an expanding map).…
Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…
We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…
Shadows encode rich information about scene geometry and illumination, yet existing methods either predict a unified shadow mask or overlook attached shadows entirely. We address this gap by proposing a framework for jointly detecting cast…
We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may…
The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this…
In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…
The present work pursues the aim to draw attention to unique possibilities of the skew-symmetric differential forms. At present the theory of skew-symmetric exterior differential forms that possess invariant properties has been developed.…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
For some involutive maps $\Phi:{\mathbb C}P^1 \times {\mathbb C}P^1 \to {\mathbb C}P^1 \times {\mathbb C}P^1$ we find all invariants with separated variables. We investigate a link of the maps and their invariants with separated variables…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
We introduce topological methods for quantifying spatially heterogeneous dynamics, and use these tools to analyze particle-tracking data for a quasi-two-dimensional granular system of air-fluidized beads on approach to jamming. In…