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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