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arXiv · 1508.07565

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

I. I. Ovsyannikov·D. V. Turaev
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Abstract

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 of 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 three-dimensional Henon-like diffeomorphisms.

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I. I. Ovsyannikov, D. V. Turaev. 2016-02-24. Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model. https://arxiv.org/abs/1508.07565

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