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

I I Ovsyannikov, D V Turaev
2016 Nonlinearity  
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
more » ... roof 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 Henonlike diffeomorphisms.
doi:10.1088/1361-6544/30/1/115 fatcat:67lpr2ocqjek7aekm77h4o2i3i