On uniform recurrence for hyperbolic automorphisms of the 2-dimensional torus
We are interested in studying sets of the form U ( α ) := { x ∈ X : ∃ M = M ( x ) ⩾ 1 such that ∀ N ⩾ M , ∃ 1 ⩽ n ⩽ N such that d ( T n x , x ) ⩽ | λ | − α N } , where ( X , T , d ) is our metric dynamical system and | λ | > 1 . Although many results exist for the one dimensional case, not as many are known for systems in higher dimensions and especially in the hyperbolic case. We consider X = T 2
