Related papers: A multi-dimensional-time dynamical system
The paper discusses the conditions for the existence of fixed points of multivalued mappings that are not based on the linear structure of the set. The descriptions for the sets of fixed points for mappings with closed graph in compact…
A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
This paper introduces a differential dynamic programming (DDP) based framework for polynomial trajectory generation for differentially flat systems. In particular, instead of using a linear equation with increasing size to represent…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…
This paper provides an algorithmic pipeline for studying the intrinsic structure of a finite discrete dynamical system (DDS) modelling an evolving phenomenon. Here, by intrinsic structure we mean, regarding the dynamics of the DDS under…
We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…
In reversible dynamical systems, it is frequently of importance to understand symmetric features. The aim of this paper is to explore symmetric periodic points of reversible maps on planar domains invariant under a reflection. We extend…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
In this article we give an overview of the concept of universal dynamics near non-thermal fixed points in isolated quantum many-body systems. We outline a non-perturbative kinetic theory derived within a Schwinger-Keldysh closed-time…
In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of…
We describe a novel method for modeling non-stationary multivariate time series, with time-varying conditional dependencies represented through dynamic networks. Our proposed approach combines traditional multi-scale modeling and network…
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…
This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…
We first consider the Hamiltonian formulation of $n=3$ systems in general and show that all dynamical systems in ${\mathbb R}^3$ are bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. We…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises…
In this paper we investigate the two dimensional dynamical system generated by the floor function with a parameter $\lambda\in \R$. We describe all limit points of the dynamical system depending on $\lambda$ and on the initial point.
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…