Related papers: On distributional chaos in non-autonomous discrete…
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…
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…
We introduce the definition of Li-Yorke chaos for the map f on G-spaces, and show G-Li-Yorke chaos is iterable for f. Li-Yorke chaos implies G-Li-Yorke chaos, while the converse is not true. Then we give a sufficient condition for f to be…
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…
We derive a semi-analytic criterion for the presence of chaos in compact, eccentric multiplanet systems. Beyond a minimum semimajor-axis separation, below which the dynamics are chaotic at all eccentricities, we show that (i) the onset of…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We prove that the set of maps which exhibit distributional chaos of type 1 (DC1) is $C^0$-dense in the space of continuous self-maps of given any compact topological manifold (possibly with boundary).
Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a…
In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of light chaos is the most significant. Severalexamples, which clarify the relationships between this kind of chaos and…
Many definitions of chaos have appeared in the last decades and with them the question if they are equivalent in some more specific spaces. Our focus will be distributional chaos, first defined in 1994 and later subdivided into three major…
It is proved that positive entropy implies mean Li-Yorke chaos for a G-system, where G is a countable infinite discrete bi-orderable amenable group. Examples are given for the cases of integer lattice groups and groups of integer unipotent…
Omega-limit sets play an important role in one-dimensional dynamics. During last fifty year at least three definitions of basic set has appeared. Authors often use results with different definition. Here we fill in the gap of missing proof…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.
We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular…
For a continuous self-map of a star graph to be Li-Yorke chaotic and to have full periodicity, we prove some new sufficient conditions on the orbit of the center.
In generic Hamiltonian systems with a mixed phase space chaotic transport may be directed and ballistic rather than diffusive. We investigate one particular model showing this behaviour, namely a spatially periodic billiard chain in which…
In this work we revisit the geometric approach to chaos in Hamiltonian dynamics, by means of the Jacobi-Levi-Civita equation (JLCE). We inspect numerically two low-dimensional dynamical systems; show that, along chaotic orbits, the…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.