Examples of Lorenz-like Attractors in Hénon-like Maps

S.V. Gonchenko; A.S. Gonchenko; I.I. Ovsyannikov; D.V. Turaev

doi:10.1051/mmnp/20138504

Geodesic

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Examples of Lorenz-like Attractors in Hénon-like Maps

S.V. Gonchenko ¹ ; A.S. Gonchenko ¹ ; I.I. Ovsyannikov ^1,² ; D.V. Turaev ²

¹ Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str. 603005 Nizhny Novgorod, Russia
² Imperial College, SW7 2 AZ London, UK

Mathematical modelling of natural phenomena, Tome 8 (2013) no. 5, pp. 48-70.

Voir la notice de l'article provenant de la source EDP Sciences

Résumé

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

DOI : 10.1051/mmnp/20138504

Affiliations des auteurs :

S.V. Gonchenko ¹ ; A.S. Gonchenko ¹ ; I.I. Ovsyannikov ^{1, 2} ; D.V. Turaev ²

¹ Research Institute of Applied Mathematics and Cybernetics, 10, Ulyanova Str. 603005 Nizhny Novgorod, Russia
² Imperial College, SW7 2 AZ London, UK

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     title = {Examples of {Lorenz-like} {Attractors} in {H\'enon-like} {Maps}},
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S.V. Gonchenko; A.S. Gonchenko; I.I. Ovsyannikov; D.V. Turaev. Examples of Lorenz-like Attractors in Hénon-like Maps. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 5, pp. 48-70. doi : 10.1051/mmnp/20138504. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138504/

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