Displaying similar documents to “On centers of type B of polynomial systems”

Totally bounded differential polynomial systems in R 2

Roberto Conti, Marcello Galeotti (2002)

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

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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.

Orbits connecting singular points in the plane

Changming Ding (2005)

Czechoslovak Mathematical Journal

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This paper concerns the global structure of planar systems. It is shown that if a positively bounded system with two singular points has no closed orbits, the set of all bounded solutions is compact and simply connected. Also it is shown that for such a system the existence of connecting orbits is tightly related to the behavior of homoclinic orbits. A necessary and sufficient condition for the existence of connecting orbits is given. The number of connecting orbits is also discussed. ...