Related papers: Genericity of distributional chaos in non-autonomo…
We study a class of singular dynamical systems which generalise the classical N-centre problem of Celestial Mechanics to the case in which the configuration space is a Riemannian surface. We investigate the existence of topological…
We consider the classical response in a chaotic system. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in a chaotic system vanishes at long times. The response also reveals certain…
A cell dynamical system model for deterministic chaos enables precise quantification of the round-off error growth,i.e., deterministic chaos in digital computer realizations of mathematical models of continuum dynamical systems. The model…
In this paper, we study continuum-wise expansive non-autonomous discrete dynamical systems. We discuss various properties of such non-autonomous systems. We further obtain results for cw-expansive non-autonomous systems with shadowing…
Topological defects are fundamental to the collective dynamics of non-equilibrium systems and in active matter, mediating spontaneous flows, dynamic self-organization, and emergent pattern formation. Here, we reveal critical states in…
A continuous map $f$ from a compact interval $I$ into itself is densely (resp. generically) chaotic if the set of points $(x,y)$ such that $\limsup_{n\to+\infty}|f^n(x)-f^n(y)|>0$ and $\liminf_{n\to+\infty} |f^n(x)-f^n(y)|=0$ is dense…
We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts whose inverse limit is not the topological factor of any effective dynamical system.…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
Distributed model predictive control methods for uncertain systems often suffer from considerable conservatism and can tolerate only small uncertainties due to the use of robust formulations that are amenable to distributed design and…
This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
A precise definition of chaos for discrete processes based on iteration already exists. We shall first reformulate it in a more general frame, taking into account the fact that discrete chaotic behavior is neither necessarily based on…
We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of "cat maps" on a two dimensional torus, and the dynamics of baker's maps. Each of these dynamics is implemented as a discrete group of…
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…
It is shown that the distributed chaos in the simple Hamiltonian (conservative) dynamical systems, such as the Nose-Hoover oscillator and double oscillator, can mimic the distributed chaos in the isotropic homogeneous turbulence. Direct…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
We demonstrate that standard delay systems with a linear instantaneous and a delayed nonlinear term show weak chaos, asymptotically subdiffusive behavior, and weak ergodicity breaking if the nonlinearity is chosen from a specific class of…
We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…
The gravitational instability of kinks is scrutinized in the context of information entropy, including the black hole formation near the scalar field critical collapse. The differential configurational entropy (DCE) is computed and examined…
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…