An example of a wild strange attractor

D. V. Turaev; L. P. Shi'nikov

doi:10.1070/sm1998v189n02abeh000300

An example of a wild strange attractor

D. V. Turaev
, L. P. Shi'nikov

Research output: Contribution to journal › Article › peer-review

91 Scopus citations

Abstract

It is proved that in the space of C^r-smooth (r ≥ 4) flows in ℝⁿ (n ≥ 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.

Original language	English
Pages (from-to)	291-314
Number of pages	24
Journal	Sbornik Mathematics
Volume	189
Issue number	1-2
DOIs	https://doi.org/10.1070/sm1998v189n02abeh000300
State	Published - 1 Jan 1998
Externally published	Yes

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1070/sm1998v189n02abeh000300

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abstract = "It is proved that in the space of Cr-smooth (r ≥ 4) flows in ℝn (n ≥ 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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AB - It is proved that in the space of Cr-smooth (r ≥ 4) flows in ℝn (n ≥ 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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An example of a wild strange attractor

Abstract

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