Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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 36 scientific papers (total in 37 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
Citations (37)
References:
PDF
HTML
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}
Linking options:
  • https://www.mathnet.ru/eng/rcd164
  • https://www.mathnet.ru/eng/rcd/v19/i4/p435
    • This publication is cited in the following 37 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024