Journal ArticleDOI
Ergodic Theory, Randomness, and "Chaos"
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TLDR
It can be shown that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation and gives a statistical analog of structural stability.Abstract:
Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of deterministic chaos. It can now be shown that this connection is more than an analogy and that at some level of abstraction a large number of systems governed by Newton's laws are the same as the baker's transformation. Going to this level of abstraction helps to organize the possible kinds of random behavior. The theory also gives new concrete results. For example, one can show that the same process could be produced by a mechanism governed by Newton's laws or by a mechanism governed by coin tossing. It also gives a statistical analog of structural stability.read more
Citations
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Journal ArticleDOI
Fast physical random bit generation with chaotic semiconductor lasers
Atsushi Uchida,Atsushi Uchida,Kazuya Amano,Masaki Inoue,Kunihito Hirano,Sunao Naito,Hiroyuki Someya,Isao Oowada,Takayuki Kurashige,Masaru Shiki,Shigeru Yoshimori,Kazuyuki Yoshimura,Peter Davis +12 more
TL;DR: It is shown that good quality random bit sequences can be generated at very fast bit rates using physical chaos in semiconductor lasers, which means that the performance of random number generators can be greatly improved by using chaotic laser devices as physical entropy sources.
Journal ArticleDOI
Complex Interactions in Metacommunities, with Implications for Biodiversity and Higher Levels of Selection
TL;DR: This computer simulation study examines the effect of complex interactions on the global and local dynamics of metacommunity dynamics, finding that complex interactions provide a new source of variation upon which natural selection can operate at the patch level, providing a mechanism for the evolution of more functionally organized communities.
Journal ArticleDOI
Statistics of chaotic binary sequences
Tohru Kohda,Akio Tsuneda +1 more
TL;DR: A simple sufficient condition for such a class of maps to produce a fair Bernoulli sequence, that is, a sequence of independent and identically distributed (i.i.d.) binary random variables.
Journal ArticleDOI
Information Flows? A Critique of Transfer Entropies.
TL;DR: It is shown that the transfer entropy and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information, and why this is the case is isolated and several avenues to alternate measures for information flow are proposed.
Journal ArticleDOI
Statistics, Probability and Chaos
TL;DR: The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, is discussed in this article. But the focus of this paper is on the mathematical models and definitions associated with chaos.
References
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Characteristic lyapunov exponents and smooth ergodic theory
TL;DR: In this article, the authors define the ergodicity of a diffeomorphism with non-zero exponents on a set of positive measure and the Bernoullian property of geodesic flows on closed Riemannian manifolds.
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Entropy and isomorphism theorems for actions of amenable groups
TL;DR: In this paper, certains des resultats fondamentaux de la theorie des isomorphismes aux actions des groupes unimodulaires moyennables generaux.
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Billiards and Bernoulli schemes
TL;DR: Some two dimensional billiards are Bernoulli flows and their consequences can be seen in the fluid dynamics of the Mississippi River.