Periodic orbits near equilibria

Luis Barreira, Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


Lyapunov,Weinstein, and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory, we establish a similar result for a differential system without assuming the existence of a first integral. Our result can also be interpreted as a kind of special Hopf bifurcation. © 2010 Wiley Periodicals, Inc.
Original languageEnglish
Pages (from-to)1225-1236
JournalCommunications on Pure and Applied Mathematics
Publication statusPublished - 1 Sept 2010


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