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- W2022067757 abstract "Inclination lemmas (λ-lemmas) serve as tools for the investigation of dynamical systems in the neighborhood of saddle points. They assert convergence of inclinations (slopes of tangents) when the system shifts a given transversal to the stable or unstable manifold towards equilibrium. We derive estimates of the speed of this convergence, for preimagesg −k (H), k∈N, of a transversalH to the unstable manifold,g is assumed to be aC 2-map in a Banach space, not necessarily reversible, with a saddle pointx=0 and already normalized so that local stable and unstable manifolds are contained in linear spaces. The estimates are needed particularly in a study of nonlocal bifurcation-from heteroclinic to periodic solutions of the second kind-for parameterized functional differential equations $$dot x(t) = ah(x(t - 1))$$ which describe phase-locked loops" @default.
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- W2022067757 date "1987-03-01" @default.
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- W2022067757 title "Inclination lemmas with dominated convergence" @default.
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- W2022067757 doi "https://doi.org/10.1007/bf00945417" @default.
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