Related papers: Infinite-Dimensional Linear Dynamical Systems with…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
We construct meta-intransitive systems of independent random variables of any finite order from basic tuple of random variables which generalize intransitive dice. Under this construction, the equality of some linear functional is…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain non-periodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in…
We utilize a recently established by the author sufficient condition for linear chaos to prove the chaoticity of derivatives in the spaces $C[a,b]$ and $L_p(a,b)$ ($-\infty<a<b<\infty$, $1\le p<\infty$).
The early-time critical dynamics of continuous, Ising-like phase transitions is studied numerically for two-dimensional lattices of coupled chaotic maps. Emphasis is laid on obtaining accurate estimates of the dynamic critical exponents…
An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
To make research of chaos more friendly with discrete equations, we introduce the concept of an unpredictable sequence as a specific unpredictable function on the set of integers. It is convenient to be verified as a solution of a discrete…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM…
Although the importance of the quantum-classical correspondence has been recognized in numerous studies of quantum chaos, whether it still holds for finite time dynamics remains less known. We address this question in this work by…
The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…
Motivated by C*-algebra theory, ultragraph edge shift spaces generalize shifts of finite type to the infinite alphabet case. In this paper we study several notions of chaos for ultragraph shift spaces. More specifically, we show that…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…
We examine some novel physical consequences of the general structure of moduli spaces of string vacua. These include (1) finiteness of the volume of the moduli space and (2) chaotic motion of the moduli in the early universe. To fix ideas…