|
This article is cited in 126 scientific papers (total in 126 papers)
An example of a wild strange attractor
D. V. Turaeva, L. P. Shilnikovb a Weierstrass Institute for Applied Analysis and Stochastics
b Research Institute for Applied Mathematics and Cybernetics, N. I. Lobachevski State University of Nizhnii Novgorod
Abstract:
It is proved that in the space of $C^r$-smooth ($r\geqslant 4$) flows in $\mathbb R^n$ ($n\geqslant 4$) there exist regions filled by systems that each have an attractor (here: a completely stable chain-transitive closed invariant set) containing a non-trivial basic hyperbolic set together with its unstable manifold, which has points of non-transversal intersection with the stable manifold. A construction is given for such a wild attractor containing an equilibrium state of saddle-focus type.
Received: 20.01.1997
Citation:
D. V. Turaev, L. P. Shilnikov, “An example of a wild strange attractor”, Sb. Math., 189:2 (1998), 291–314
Linking options:
https://www.mathnet.ru/eng/sm300https://doi.org/10.1070/sm1998v189n02ABEH000300 https://www.mathnet.ru/eng/sm/v189/i2/p137
|
Statistics & downloads: |
Abstract page: | 1524 | Russian version PDF: | 572 | English version PDF: | 52 | References: | 95 | First page: | 2 |
|