Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
File(s)1508.07565v2.pdf (287.57 KB)
Accepted version
Author(s)
Ovsyannikov, II
Turaev, D
Type
Journal Article
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.
Date Issued
2016-11-22
Date Acceptance
2016-11-03
ISSN
1361-6544
Publisher
IOP Publishing
Start Page
115
End Page
137
Journal / Book Title
Nonlinearity
Volume
30
Issue
1
Copyright Statement
© 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/10.1088/1361-6544/30/1/115
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000389254300002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
Lorenz attractor
Henon map
homoclinic butterfly
separatrix value
HENON-LIKE MAPS
HOMOCLINIC BIFURCATION
TRANSITIVE ATTRACTOR
GLOBAL BIFURCATIONS
DIFFEOMORPHISMS
CHAOS
SYSTEMS
POINTS
math.DS
34D45, 37C70, 37D45, 37C29
General Mathematics
0102 Applied Mathematics
Publication Status
Published