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Chaos An Interdisciplinary Journal of Nonlinear Science
Article . 2015 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Article . 2015
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https://dx.doi.org/10.48550/ar...
Article . 2015
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Defining chaos

Authors: Hunt, Brian R.; Ott, Edward;
Abstract

In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call “expansion entropy,” and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

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Keywords

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to dynamical systems and ergodic theory, FOS: Mathematics, FOS: Physical sciences, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, Strange attractors, chaotic dynamics of systems with hyperbolic behavior

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
42
Top 10%
Top 10%
Top 10%
Green
hybrid