Proc. of Institute of mathematics and mechanics, 2015, Volume 41, Issue 1, paper published in the English version journal
Trajectories that have points at infinity as limit sets for dynamical systems on the plane
Maxim V. Shamolin
Lomonosov Moscow State University, Institute of Mechanics
In this paper, we deal with the existence and uniqueness of
trajectories of the dynamical systems on the plane that have
infinitely remote points as $\alpha$- and $\omega$-limit sets.
Therefore, on the Riemann or Poincaré sphere, the limit set of
such trajectories is the north pole. These are key trajectories by
definition since an infinitely remote point is always singular.
MSC: 37C, 70E
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