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

Authors
  • Ovsyannikov, II
  • Turaev, D
Publication Date
Nov 03, 2016
Identifiers
DOI: 10.1088/1361-6544/30/1/115
OAI: oai:spiral.imperial.ac.uk:10044/1/43895
Source
Spiral - Imperial College Digital Repository
Keywords
License
Unknown

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 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.

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