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Moscow Mathematical Journal, 2011, Volume 11, Number 3, Pages 413–438 (Mi mmj425)  

Generalised Hopf bifurcations: a birth lemma

Marc Chaperon

Institut de mathématiques de Jussieu & IMCCE, Université Paris Diderot – Paris 7, UFR de Mathématiques, Paris, France
References:
Abstract: We state and prove a “birth lemma” generalising the Poincaré–Andronov–Hopf and Sacker–Naimark bifurcation theorems. It implies the birth of many topologically different compact invariant manifolds in generic families of dynamics depending on at least two parameters.
Key words and phrases: Arnold, Thom, bifurcation, Hopf, Sacker–Naimark, normally hyperbolic, moment-angle manifolds, catastrophe, coupling.
Received: February 16, 2011
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Document Type: Article
Language: English
Citation: Marc Chaperon, “Generalised Hopf bifurcations: a birth lemma”, Mosc. Math. J., 11:3 (2011), 413–438
Citation in format AMSBIB
\Bibitem{Cha11}
\by Marc~Chaperon
\paper Generalised Hopf bifurcations: a~birth lemma
\jour Mosc. Math.~J.
\yr 2011
\vol 11
\issue 3
\pages 413--438
\mathnet{http://mi.mathnet.ru/mmj425}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2894423}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000300365900001}
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