Hausdorff dimension of recurrence sets
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 } .