Relatório de pesquisa 15/08


Hopf bifurcation for vector fields in $R^4$ with pure imaginary eigenvalues in resonance 1:2 and 3:2, Jaume Llibre and Ana Cristina Mereu, submitted Sept. 04.

Abstract
Assume that the linear part at a singular point of a C^k differential system with k=3,4,5 in R^4 has pure imaginary eigenvalues in resonance 1:2 when k=3,4 and in resonance 2:3 when k=5. If k=3 from this singular point it can bifurcate 0 or 1 one-parameter family of periodic orbits. If k=4 it can bifurcate 0, 1, 2, 3 or 4 one-parameter families of periodic orbits and if k=5 it can bifurcate 0, 1, 2, 3, 4, 5 or 6 one-parameter families of periodic orbits. The tool for proving such a result is the averaging theory.


Mathematics Subject Classifications (2000):  34C29, 34C25, 47H11.

Keywords:
limit cycle, periodic orbit, Hopf bifurcation, Liapunov center theorem, averaging theory, resonance 1:2, resonance 3:2.


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September 04, 2008

 

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