Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
Dynamical Systems
2016-02-25 v2
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.
Keywords
Cite
@article{arxiv.1508.07565,
title = {Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model},
author = {I. I. Ovsyannikov and D. V. Turaev},
journal= {arXiv preprint arXiv:1508.07565},
year = {2016}
}