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A test for a conjecture on the nature of attractors for smooth dynamical systems
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Gottwald, Georg A. and Melbourne, Ian (2014) A test for a conjecture on the nature of attractors for smooth dynamical systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, Volume 24 (Number 2). Article number 024403. doi:10.1063/1.4868984 ISSN 1054-1500.
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Official URL: http://dx.doi.org/10.1063/1.4868984
Abstract
Dynamics arising persistently in smooth dynamical systems ranges from regular dynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov, uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). The latter include many classical examples such as Lorenz and Hénon-like attractors and enjoy strong statistical properties. It is natural to conjecture (or at least hope) that most dynamical systems fall into these two extreme situations. We describe a numerical test for such a conjecture/hope and apply this to the logistic map where the conjecture holds by a theorem of Lyubich, and to the 40-dimensional Lorenz-96 system where there is no rigorous theory. The numerical outcome is almost identical for both (except for the amount of data required) and provides evidence for the validity of the conjecture.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Chaos: An Interdisciplinary Journal of Nonlinear Science | ||||
Publisher: | American Institute of Physics | ||||
ISSN: | 1054-1500 | ||||
Official Date: | 2014 | ||||
Dates: |
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Volume: | Volume 24 | ||||
Number: | Number 2 | ||||
Article Number: | Article number 024403 | ||||
DOI: | 10.1063/1.4868984 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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