Ovsyannikov, IIIIOvsyannikovTuraev, DDTuraev2017-02-012017-11-222016-11-22Nonlinearity, 2016, 30 (1), pp.115-1371361-6544http://hdl.handle.net/10044/1/43895We 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.© 2016 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at http://dx.doi.org/10.1088/1361-6544/30/1/115Science & TechnologyPhysical SciencesMathematics, AppliedPhysics, MathematicalMathematicsPhysicsLorenz attractorHenon maphomoclinic butterflyseparatrix valueHENON-LIKE MAPSHOMOCLINIC BIFURCATIONTRANSITIVE ATTRACTORGLOBAL BIFURCATIONSDIFFEOMORPHISMSCHAOSSYSTEMSPOINTSmath.DS34D45, 37C70, 37D45, 37C29General Mathematics0102 Applied MathematicsJournal Articlehttps://www.dx.doi.org/10.1088/1361-6544/30/1/115