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July  1997, 3(3): 401-418. doi: 10.3934/dcds.1997.3.401

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

Paolo Perfetti 1,

1. 

Dipartimento di matematica II Università di Roma, via della Ricerca Scientifica 00133 Roma, Italy

Received  December 1996 Published  April 1997

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.
Keywords: periodic solutions, implicit function theorem., Poincaré's continuation method, dynamical systems.
Mathematics Subject Classification: 26B10, 34A15, 34C1.
Citation: Paolo Perfetti. An infinite-dimensional extension of a Poincaré's result concerning the continuation of periodic orbits. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 401-418. doi: 10.3934/dcds.1997.3.401
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