Related papers: What Are the New Implications of Chaos for Unpredi…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic,…
A source of unpredictability is equivalent to a source of information: unpredictability means not knowing which of a set of alternatives is the actual one; determining the actual alternative yields information. The degree of…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is…
Recently, a new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of physics itself such as determinism, causality, free will, predictability, and irreversibility [J. Phys. Soc. Jpn. {\bf 79},…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
General relativity exhibits a unique feature not represented in standard examples of chaotic systems; it is a spacetime diffeomorphism invariant theory. Thus many characterizations of chaos do not work. It is therefore necessary to develop…
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…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
To make research of chaos more friendly with discrete equations, we introduce the concept of an unpredictable sequence as a specific unpredictable function on the set of integers. It is convenient to be verified as a solution of a discrete…
We propose a new approach to define chaos in dynamical systems from the point of view of Information Dynamics. Observation of chaos in reality depends upon how to observe it, for instance, how to take the scale in space and time. Therefore…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…
The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and…
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…
Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the…
In paper [1] unpredictable points were introduced based on Poisson stability, and this gives rise to the existence of chaos in the quasi-minimal set. This time, an unpredictable function is determined as an unpredictable point in the…