A polynomial -system with the limit set consisting of four heteroclinic trajectories
A polynomial -system with the limit set consisting of four heteroclinic trajectories
Abstract
The limit set of a dynamical system plays an important role in studying its global behavior. It is
proved that bounded limit set is a continuum i.e. connected and compact [1, 3, 8]. However, unbounded
limit set may have enough complicated structure even for quadratic system [1-10]. We will give an
example of the polynomial system in the space , such that the -limit set of some trajectory consists
of four heteroclinic trajectories.
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