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 Proc. of Institute of mathematics and mechanics: Year: Volume: Issue: Page: Find

 Proc. of Institute of mathematics and mechanics, 2015, Volume 41, Issue 1, paper published in the English version journal (Mi pazan15)

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

Abstract: 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.

Document Type: Article
MSC: 37C, 70E
Accepted:16.05.2015
Language: English