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Generalised Hopf bifurcations: a birth lemma
Marc Chaperon Institut de mathématiques de Jussieu & IMCCE, Université Paris Diderot – Paris 7, UFR de Mathématiques, Paris, France
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
Citation:
Marc Chaperon, “Generalised Hopf bifurcations: a birth lemma”, Mosc. Math. J., 11:3 (2011), 413–438
Linking options:
https://www.mathnet.ru/eng/mmj425 https://www.mathnet.ru/eng/mmj/v11/i3/p413
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Abstract page: | 186 | References: | 48 |
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