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.
Original language | English |
---|---|
Pages (from-to) | 115-137 |
Number of pages | 23 |
Journal | Nonlinearity |
Volume | 30 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2017 |
Externally published | Yes |
Keywords
- Henon map
- Lorenz attractor
- homoclinic butterfly
- separatrix value
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics