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Mat. Sb., 1998, Volume 189, Number 2, Pages 137–160 (Mi msb300)  

This article is cited in 73 scientific papers (total in 73 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.


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English version:
Sbornik: Mathematics, 1998, 189:2, 291–314

Bibliographic databases:

UDC: 517.95
MSC: Primary 58F14; Secondary 58F13, 58F15, 58F25, 58F14, 58F12, 58F10, 34C37, 3
Received: 20.01.1997

Citation: D. V. Turaev, L. P. Shilnikov, “An example of a wild strange attractor”, Mat. Sb., 189:2 (1998), 137–160; Sb. Math., 189:2 (1998), 291–314

Citation in format AMSBIB
\by D.~V.~Turaev, L.~P.~Shilnikov
\paper An example of a wild strange attractor
\jour Mat. Sb.
\yr 1998
\vol 189
\issue 2
\pages 137--160
\jour Sb. Math.
\yr 1998
\vol 189
\issue 2
\pages 291--314

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