Abstract
Abstract
We consider linear mappings on the 2-dimensional torus, defined by
T
(
x
)
=
A
x
(
mod
1
)
, where A is an invertible
2
×
2
integer matrix, with no eigenvalues on the unit circle. In the case
det
A
=
±
1
, we give a formula for the Hausdorff dimension of the set
{
x
∈
T
2
:
d
(
T
n
(
x
)
,
x
)
<
e
−
α
n
for infinitely many
n
}
.
Funder
China Scholarship Council
Science Foundation of China University of Petroleum, Beijing