ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXII, 1(2003)
p. 81 110

Unbounded Basins of Attraction of Limit Cycles
P. Giesl


Abstract.  Consider a dynamical system given by a system of autonomous ordinary differential equations. In this paper we provide a sufficient local condition for an unbounded subset of the phase space to belong to the basin of attraction of a limit cycle. This condition also guarantees the existence and uniqueness of such a limit cycle, if that subset is compact. If the subset is unbounded, the positive orbits of all points of this set either are unbounded or tend to a unique limit cycle.

AMS subject classification:  37C27, 34D05, 34C25, 34C05
Keywords:  Dynamical system, periodic orbit, basin of attraction

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