Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Obstruction theory and multiparameter Hopf bifurcation


Author: Jorge Ize
Journal: Trans. Amer. Math. Soc. 289 (1985), 757-792
MSC: Primary 58E07; Secondary 55S35, 58F22
MathSciNet review: 784013
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Hopf bifurcation problem is treated as an example of an equivariant bifurcation. The existence of a local bifurcating solution is given by the nonvanishing of an obstruction to extending a map defined on a complex projective space and is computed using the complex Bott periodicity theorem. In the case of the classical Hopf bifurcation the results of Chow, Mallet-Paret and Yorke are recovered without using any special index as the Fuller degree: There is bifurcation if the number of exchanges of stability is nonzero. A global theorem asserts that the sum of the local invariants on a bounded component of solutions must be zero.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58E07, 55S35, 58F22

Retrieve articles in all journals with MSC: 58E07, 55S35, 58F22


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0784013-2
PII: S 0002-9947(1985)0784013-2
Keywords: Hopf bifurcation, equivariant obstruction
Article copyright: © Copyright 1985 American Mathematical Society