On Invariant Sets of Diffeomorphisms
  We give a simple upper bound for the upper box dimension of a backward invariant set of a $C^{1}$-diffeomorphism of a Riemannian manifold. We also estimate an upper bound for the box dimension of a forward invariant set of a $C^{1}$-mapping with finite Brouwer degree in a Riemannian manifold. 
Mehrzad Monzavi and Reza Mirzaei
math.DS