Related papers: Generic and dense distributional chaos with shadow…
This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…
Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of $\R^N$, whose most familiar example is provided by the $N-$dimensional torus $\T ^N$. It is proved that…
We introduce the concept of a class of equivalence of molecular clouds represented by an abstract spherically symmetric, isotropic object. This object is described by use of abstract scales in respect to a given mass density distribution.…
Using the decoherence formalism of Gell-Mann and Hartle, a quantum system is found which is the equivalent of the classical chaotic Duffing oscillator. The similarities and the differences from the classical oscillator are examined; in…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We introduce a general approach to characterize composite fading models based on inverse gamma (IG) shadowing. We first determine to what extent the IG distribution is an adequate choice for modeling shadow fading, by means of a…
This work is devoted to the formulation and derivation of the $\eta{-}\mu{/}$gamma and $\lambda{-}\mu{/}$gamma distributions which correspond to physical fading models. These distributions are composite and are based on the $\eta-\mu$ and…
We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the…
For any continuous self-map of a compact metric space, we provide sufficient conditions under which the infinite direct product of the map is $\omega$-chaotic. We also apply the result to obtain some examples of unusual $\omega$-chaotic…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
This paper shows that the recently proposed $\kappa$-$\mu$ shadowed fading model includes, besides the $\kappa$-$\mu$ model, the $\eta$-$\mu$ fading model as a particular case. This has important relevance in practice, as it allows for the…
We prove that both multiple Rademacher system and Rademacher chaos possess the property of random unconditional convergence in the space $L_\infty$. This fact combined with some intimate connections between $L_\infty$-norms of linear…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the…
Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
We study the mean orbital pseudo-metric for Polish dynamical systems and its connections with properties of the space of invariant measures. We give equivalent conditions for when the set of invariant measures generated by periodic points…