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Examples of Lorenz-like Attractors in Hénon-likeMaps

Published online by Cambridge University Press:  17 September 2013

S.V. Gonchenko ,
A.S. Gonchenko ,
I.I. Ovsyannikov  and
D.V. Turaev
S.V. Gonchenko*
Affiliation:
Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str. 603005 Nizhny Novgorod, Russia
A.S. Gonchenko
Affiliation:
Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str. 603005 Nizhny Novgorod, Russia
I.I. Ovsyannikov
Affiliation:
Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str. 603005 Nizhny Novgorod, Russia Imperial College, SW7 2 AZ London, UK
D.V. Turaev
Affiliation:
Imperial College, SW7 2 AZ London, UK
*
⋆ Corresponding author. E-mail: gonchenko@pochta.ru
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Abstract

We display a gallery of Lorenz-like attractors that emerge in a class ofthree-dimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms(as opposed to flows), define various types of such attractors, and find sufficientconditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-likeattractors. The numerically obtained scenarios of the creation and destruction of theseattractors are also presented.

Keywords

Strange attractorthree-dimensional mapspseudohyperbolicityvolume hyperbolicitybifurcationshomoclinic orbithomoclinic tangencywild setnormal form
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 48 - 70
Copyright
© EDP Sciences, 2013

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