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Generic Hopf bifurcation from lines of equilibria without parameters. I: Theory. (English) Zbl 0978.34035
Real autonomous systems of ordinary differential equations are considered having a line of equilibria and satisfying additional nondegeneracy conditions. The loss of stability along this line is investigated in cases of one real/a couple of complex conjugate eigenvalues crossing the imaginary axis. Based on the corresponding 2/3-dimensional normal forms the behavior of close trajectories is presented. The investigation of the problem is motivated by several applications.

MSC:
34C23 Bifurcation theory for ordinary differential equations
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
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