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Nonautonomous bifurcation of bounded solutions I: A Lyapunov-Schmidt approach
| 1. | Technische Universität München, Zentrum Mathematik, Boltzmannstraße 3, D-85758 Garching, Germany |
Under this premise, appropriate exponential dichotomies in the variational equation along a nonhyperbolic solution on both time axes provide the necessary Fredholm theory in order to employ a Lyapunov-Schmidt reduction. Among other results, this yields nonautonomous versions of the classical fold, transcritical and pitchfork bifurcation patterns.
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