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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 2 (1990), S. 177-244 
    ISSN: 1572-9222
    Keywords: homoclinic orbit ; period doubling ; pathfollowing ; global bifurcation ; resonance ; 34C15 ; 34C35 ; 58F14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a bifurcation of homoclinic orbits, which is an analogue of period doubling in the limit of infinite period. This bifurcation can occur in generic two parameter vector fields when a homoclinic orbit is attached to a stationary point with resonant eigenvalues. The resonance condition requires the eigenvalues with positive/negative real part closest to zero to be real, simple, and equidistant to zero. Under an additional global twist condition, an exponentially flat bifurcation of double homoclinic orbits from the primary homoclinic branch is established rigorously. Moreover, associated period doublings of periodic orbits with almost infinite period are detected. If the global twist condition is violated, a resonant side switching occurs. This corresponds to an exponentially flat bifurcation of periodic saddle-node orbits from the homoclinic branch.
    Type of Medium: Electronic Resource
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