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Article Contents

# An infinite-dimensional extension of a Poincaré's result concerning the continuation of periodic orbits

• We study the existence of periodic solutions for the infinite-dimensional second order system $\ddot x=V_{x},\ x\in\mathbb{T}^{\mathbb{Z}_+}.$ Using the Implicit-Function-Theorem, we prove the existence of time-periodic solutions at "high frequencies"; no "smallness condition" on $V(x)$ is required.
Mathematics Subject Classification: 26B10, 34A15, 34C15.

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