This paper is concerned with invariance (F1,F2)-scrambled sets under iterations. The main results are an extension of the compound invariance of Li–Yorke chaos and distributional chaos. New definitions of (F1,F2)-scrambled sets in non-autonomous discrete systems are given. For a positive integer k, the properties P(k) and Q(k) of Furstenberg families are introduced. It is shown that, for any po...

Let (X, ‖ · ‖) be a Banach space, f : X → X continous Freche’t differentiable map.Denote the set of almost periodic point by A(f).In this paper,we prove that there exists an uncountable set Λ such that f |Λ is distributionally chaotic,and Λ ⊂ A(f).

This paper provides an overview of computationally efficient approaches for quantifying the influence of parameter uncertainties on the states and outputs of nonlinear dynamical systems with finite-time control trajectories, focusing primarily on computing probability distributions. The advantages and disadvantages of various uncertainty analysis approaches, which use approximate representation...

According to the recurrent frequency, many levels of points are found such as periodic points, almost weakly quasi-weakly and Banach points. In this paper, we consider symbolic dynamics show existence six refined between recurrence general recurrence. Despite fact that these all null-measure under any invariant measure, further they carry strong topological complexity. Each level is dense in wh...

[1] Distributional analysis of river discharge time series is an important task in many areas of hydrological engineering, including optimal design of water storage and drainage networks, management of extreme events, risk assessment for water supply, and environmental flow management, among many others. Having diverging moments, heavy-tailed power law distributions have attracted widespread at...

Over the last decades the research on monetary policy has largely concentrated on the impact of monetary authorities’ decisions on inflation and the fine-tuning of the macroeconomic, so that distributional effects of monetary policy which are non-trivial has been ignored. A view that has become increasingly popular since the financial crisis 2008 is that expansionary monetary policy can exacerb...

We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising combinatorial complexity by means of the moments/cumulants duality for the laws of the corresponding processes, themselves measures on distributional spaces, and pr...

Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...