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Regular and Chaotic Dynamics, 2014, Volume 19, Issue 4, Pages 435–460
DOI: https://doi.org/10.1134/S1560354714040017 (Mi rcd164) 		 
This article is cited in 35 scientific papers (total in 36 papers)

Scientific Heritage of L.P. Shilnikov

Valentin S. Afraimovicha, Sergey V. Gonchenkob, Lev M. Lermanb, Andrey L. Shilnikovbc, Dmitry V. Turaevd

a Universidad Autónoma de San Luis Potosí, Av. Karakorum 1470, Lomas 4a. San Luis Potosí, 78210, México
b Lobachevsky State University of Nizhny Novgorod, pr. Gagarina 23, Nizhny Novgorod, 603950 Russia
c Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta 30303, USA
d Imperial College, SW7 2 AZ London, UK
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DOI: https://doi.org/10.1134/S1560354714040017
Abstract: This is the first part of a review of the scientific works of L.P. Shilnikov. We group his papers according to 7 major research topics: bifurcations of homoclinic loops; the loop of a saddle-focus and spiral chaos; Poincare homoclinics to periodic orbits and invariant tori, homoclinic in noautonous and infinite-dimensional systems; Homoclinic tangency; Saddlenode bifurcation — quasiperiodicity-to-chaos transition, blue-sky catastrophe; Lorenz attractor; Hamiltonian dynamics. The first two topics are covered in this part. The review will be continued in the further issues of the journal.
Keywords: Homoclinic chaos, global bifurcations, spiral chaos, strange attractor, saddle-focus, homoclinic loop, saddle-node, saddle-saddle, Lorenz attractor, hyperbolic set.
Received: 01.07.2014
Accepted: 11.07.2014
Bibliographic databases:
Document Type: Article
MSC: 37-01, 37-02, 01A65, 37C29, 37D45
Language: English
Citation: Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev, “Scientific Heritage of L.P. Shilnikov”, Regul. Chaotic Dyn., 19:4 (2014), 435–460
Citation in format AMSBIB
\Bibitem{AfrGonLer14}
\by Valentin~S.~Afraimovich, Sergey~V.~Gonchenko, Lev~M.~Lerman, Andrey~L.~Shilnikov, Dmitry~V.~Turaev
\paper Scientific Heritage of L.P. Shilnikov
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 4
\pages 435--460
\mathnet{http://mi.mathnet.ru/rcd164}
\crossref{https://doi.org/10.1134/S1560354714040017}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3240978}
\zmath{https://zbmath.org/?q=an:06392357}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000340380900001}
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  • https://www.mathnet.ru/eng/rcd/v19/i4/p435
    • This publication is cited in the following 36 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:49
     
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