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Homoclinic bifurcation at resonant eigenvalues. (English) Zbl 0703.34050
From the summary: The authors consider a bifurcation of homoclinic orbits, which is an analogue of periodic doubling in the limit of infinite period. The resonance condition requires the eigenvalues with positive/negative real part closest to zero to be real, simple, and equidistant to zero. Under some conditions, an exponentially flat bifurcation of double homoclinic orbits from the primary homoclinic branch is established rigorously. This bifurcation can occur in generic two parameter vector fields when a homoclinic orbit is attached to a stationary point with resonant eigenvalues. This paper contains two new theorems and a wide discussion of the problem under consideration.
Reviewer: D.Bobrowski

34C15Nonlinear oscillations, coupled oscillators (ODE)
37-99Dynamic systems and ergodic theory (MSC2000)
37G99Local and nonlocal bifurcation theory
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