Related papers: Distinguished trajectories in time dependent vecto…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Differential drive robots are widely used in various scenarios thanks to their straightforward principle, from household service robots to disaster response field robots. There are several types of driving mechanisms for real-world…
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation of phase space with an additional time…
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
We prove structural stability under perturbations for a class of discrete-time dynamical systems near a non-hyperbolic fixed point. We reformulate the stability problem in terms of the well-posedness of an infinite-dimensional nonlinear…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…
Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
We introduce the concept of a deterministic walk. Confining our attention to the finite state case, we establish hypotheses that ensure that the deterministic walk is transitive, and show that this property is in some sense robust. We also…
Let $(X,f_{1,\infty})$ be a nonautonomous dynamical system. In this paper we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new, very natural, definition of asymptotic periodicity.…
This work constructs symbolic dynamics for non-uniformly hyperbolic surface maps with a set of discontinuities $D$. We allow the derivative of points nearby $D$ to be unbounded, of the order of a negative power of the distance to $D$. Under…
The main purpose of this article is to study box dimension of orbits near hyperbolic and nonhyperbolic fixed points of discrete dynamical systems in higher dimensions. We generalize the known results for one-dimensional systems, that is,…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Simple models of irreversible dynamical processes such as Bootstrap Percolation have been successfully applied to describe cascade processes in a large variety of different contexts. However, the problem of analyzing non-typical…
This article presents a new algorithm, the Hyperbolic and Elliptic Points Tracking Algorithm (HEPTA), designed for automated tracking of elliptic and hyperbolic stationary points in two-dimensional non-stationary velocity fields defined on…