Related papers: Devaney Chaos on a Set-valued Map and Its Inverse …
The Gauss map (or continued fraction map) is an important dissipative one-dimensional discrete-time dynamical system that exhibits chaotic behaviour and which generates a symbolic dynamics consisting of infinitely many different symbols.…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…
The mixing properties (or sensitivity to initial conditions) and relaxation dynamics of the Henon map, together with the connection between these concepts, have been explored numerically at the edge of chaos. It is found that the results…
Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets…
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
Irreversible Port Hamiltonian Systems are departure of Port Hamiltonian Systems as they are generated not only by a Hamiltonian function but also by an entropy function and defined with respect to a quasi-Poisson bracket which embeds the…
We propose a handful of definitions of injectivity for a parametrized family of maps and study its link with a global nonuniform stability conjecture for nonautonomous differential systems, which has been recently introduced. This relation…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
We show that a uniformly continuous random perturbation of a transitive map defines an aperiodic Harris chain which also satisfies Doeblin's condition. As a result, we get exponential decay of correlations for suitable random perturbations…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
In this paper, we consider inverse limits of [0,1] using upper semicontinuous set-valued bonding functions with the intermediate value property. Expanding on classical results by Barge and Martin, we explore the relationship between…
The paper considers a stabilizing stochastic control which can be applied to a variety of unstable and even chaotic maps. Compared to previous methods introducing control by noise, we relax assumptions on the class of maps, as well as…
Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has…
It is argued that, if a regular Hamiltonian is perturbed by a term that produces chaos, the onset of chaos is shifted towards larger values of the perturbation parameter if the unperturbed spectrum is degenerate and the lifting of the…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves…
A famous aspect of discrete dynamical systems defined by area-preserving maps is the physical interpretation of stochastic transitions occurring locally which manifest themselves through the destruction of invariant KAM curves and the local…