| Issue |
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
|
|
|---|---|---|
| Page(s) | 48 - 70 | |
| DOI | https://doi.org/10.1051/mmnp/20138504 | |
| Published online | 17 September 2013 | |
Examples of Lorenz-like Attractors in Hénon-like Maps
1
Research Institute of Applied Mathematics and
Cybernetics, 10, Ulyanova
Str.
603005
Nizhny Novgorod,
Russia
2
Imperial College, SW7 2
AZ London,
UK
⋆ Corresponding author. E-mail: gonchenko@pochta.ru
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.
Mathematics Subject Classification: 34D45 / 37C70 / 37D45
Key words: Strange attractor / three-dimensional maps / pseudohyperbolicity / volume hyperbolicity / bifurcations / homoclinic orbit / homoclinic tangency / wild set / normal form
© EDP Sciences, 2013
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