On two-dimensional surface attractors and repellers on 3-manifolds
Abstract
We show that if
f:
M
3
→
M
3
is an
A
-diffeomorphism with a surface two-dimensional attractor or repeller
B
and
M
2
B
is a supporting surface for
B
, then
B=
M
2
B
and there is
k≥1
such that: 1)
M
2
B
is a union
M
2
1
∪...∪
M
2
k
of disjoint tame surfaces such that every
M
2
i
is homeomorphic to the 2-torus
T
2
. 2) the restriction of
f
k
to
M
2
i
(i∈{1,...,k})
is conjugate to Anosov automorphism of
T
2
.