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Totally bounded differential polynomial systems in R 2

Roberto ContiMarcello Galeotti — 2002

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Totally bounded differential systems in R 2 are defined as having all trajectories bounded. By Dulac’s finiteness theorem it is proved that totally bounded polynomial systems exhibit an unbounded «annulus» of cycles. The portrait of the remaining trajectories is examined in the case the system has, in R 2 , a unique singular point. Work is in progress concerning the study of totally bounded polynomial systems with two singular points.

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