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Mathematics of the USSR-Sbornik, 1992, Volume 73, Issue 2, Pages 415–443
DOI: https://doi.org/10.1070/SM1992v073n02ABEH002553
(Mi sm1340)
 

This article is cited in 58 scientific papers (total in 58 papers)

Systems with a homoclinic curve of multidimensional saddle-focus, and spiral chaos

I. M. Ovsyannikov, L. P. Shilnikov
References:
Abstract: Consider the space $\mathscr B^1$ of dynamical systems having an isolated equilibrium point $O$ of saddle-focus type with a one- or two-dimensional unstable manifold and a trajectory $\Gamma$ homoclinic at $O$.
The following results are proved:
1. Systems with structurally unstable periodic motions are dense in $\mathscr B^1$.
2. Systems with a countable set of stable periodic motions are dense in the open subset $\mathscr B^1_s$ of $\mathscr B^1$ comprised of systems whose second saddle parameter $\sigma_2$ is negative.
3. Neither the subset $\mathscr B^1_u$ of $\mathscr B^1$ consisting of systems satisfying $\sigma_2>0$ nor any sufficiently small neighborhood of $\mathscr B^1_u$ in the space of all dynamical systems contains a system with stable periodic motions in a sufficiently small neighborhood of the contour $O\cup\Gamma$.
Received: 09.04.1990
Bibliographic databases:
UDC: 517.9
MSC: Primary 58F13; Secondary 34D30, 70K15, 34C37
Language: English
Original paper language: Russian
Citation: I. M. Ovsyannikov, L. P. Shilnikov, “Systems with a homoclinic curve of multidimensional saddle-focus, and spiral chaos”, Math. USSR-Sb., 73:2 (1992), 415–443
Citation in format AMSBIB
\Bibitem{OvsShi91}
\by I.~M.~Ovsyannikov, L.~P.~Shilnikov
\paper Systems with a~homoclinic curve of multidimensional saddle-focus, and spiral chaos
\jour Math. USSR-Sb.
\yr 1992
\vol 73
\issue 2
\pages 415--443
\mathnet{http://mi.mathnet.ru//eng/sm1340}
\crossref{https://doi.org/10.1070/SM1992v073n02ABEH002553}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1128258}
\zmath{https://zbmath.org/?q=an:0774.58030|0741.58031}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992SbMat..73..415O}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992KF43400007}
Linking options:
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  • https://doi.org/10.1070/SM1992v073n02ABEH002553
  • https://www.mathnet.ru/eng/sm/v182/i7/p1043
  • This publication is cited in the following 58 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник - 1991 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:599
    Russian version PDF:183
    English version PDF:35
    References:60
    First page:1
     
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