On the Poincar Map of the Almost-Periodic Oscillation of the Periodically Excited Linard System

Tosiro KOGA  Masaharu SHINAGAWA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E74-A   No.6   pp.1401-1405
Publication Date: 1991/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Issue on Nonlinear Theory and Its Applications)

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This paper clarifies some properties of the Poincar map of the almost periodic oscillation, which is generated by a periodically excited nonlinear system described by a Linard equation. Arguments in this paper are based on the extended Linard theorem already published by the present authors and are focused on the almost periodic oscillations which may occur in the Linard system under a certain constraint on the external force. As the main result, it is shown that the Poincar map of the almost periodic oscillation drawn on the Linard plane forms a simple closed continuous curve, under an explicitly given condition on the external force e (t) = A sin (ωt+θ), for arbitrary value of the amplitude A except for a set of the values ω with zero measure.