Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model

We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous ve...

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Bibliographic Details
Published in:Nonlinearity 2017-01, Vol.30 (1), p.115-137
Main Authors: Ovsyannikov, I I, Turaev, D V
Format: Article
Language:English
Subjects:
Henon map
homoclinic butterfly
Lorenz attractor
separatrix value
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Summary:We give an analytic (free of computer assistance) proof of the existence of a classical Lorenz attractor for an open set of parameter values of the Lorenz model in the form of Yudovich-Morioka-Shimizu. The proof is based on detection of a homoclinic butterfly with a zero saddle value and rigorous verification of one of the Shilnikov criteria for the birth of the Lorenz attractor; we also supply a proof for this criterion. The results are applied in order to give an analytic proof for the existence of a robust, pseudohyperbolic strange attractor (the so-called discrete Lorenz attractor) for an open set of parameter values in a 4-parameter family of 3D Henon-like diffeomorphisms.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/30/1/115