Abstract
Let
H
n
be the maximum possible number of limit cycles of systems
ẋ
=
P
(
x
,
y
),
ẏ
=
Q
(
x
,
y
), where
P
and
Q
are polynomials of degree at most
n
. We are concerned with the rate of growth of
H
n
as
n
increases: it is known that
H
n
≽
kn
2
for some constant
k
. In this paper we show that
H
n
grows at least as rapidly as
n
2
log
n
.
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