Abstract
The aim of the present paper is to study the structure of the nonwandering set of points
Ω
(
⋅
)
for the skew-product maps
C
Δ
∗
(
I
2
)
of the unit square
I
2
=
[
0
,
1
]
×
[
0
,
1
]
,
(
x
,
y
)
→
(
f
(
x
)
,
g
(
x
,
y
)
)
, with base
f having closed set of periodic points. For every
F
∈
C
Δ
∗
(
I
2
)
and every point
(
x
,
y
)
with
x periodic of period
p
x
by
f and
y not chain recurrent of
F
p
x
|
I
x
, where
I
x
=
{
x
}
×
I
, we prove that
(
x
,
y
)
∉
Ω
(
F
)
. On the other hand we construct a map
F
0
∈
C
Δ
∗
(
I
2
)
with an isolated fixed point
x
0
of
f and
y
0
∉
Ω
(
F
|
I
x
0
)
such that
(
x
0
,
y
0
)
∈
Ω
(
F
0
)
.