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

@inproceedings{Ovsyannikov2015AnalyticPO, title={Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model}, author={I. I. Ovsyannikov and Dmitry Turaev}, year={2015} }

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… CONTINUE READING

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