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Better bounds for periodic solutions of differential equations in Banach spaces. (English) Zbl 0632.34048
Let B be a Banach space, let f:BB be Lipschitz with constant L and let x be a P-periodic solution of x ' (t)=f(x(t)). The authors prove that LP6, thus improving earlier work of A. Lasota and J. Yorke [J. Differ. Equations 10, 83-91 (1971; Zbl 0261.34035)] who were the first to consider this question. They also give a short proof of the (known, sharp) inequality LP2π when B is a Hilbert space. In a “Note added in proof” they claim to have constructed an example, in a Banach-space setting, in which LP=6.
Reviewer: D.E.Edmunds

34C25Periodic solutions of ODE
34C45Invariant manifolds (ODE)