An elementary way to rigorously estimate convergence to equilibrium and   escape rates
  We show an elementary method to have (finite time and asymptotic) computer assisted explicit upper bounds on convergence to equilibrium (decay of correlations) and escape rate for systems satisfying a Lasota Yorke inequality. The bounds are deduced by the ones of suitable approximations of the system's transfer operator. We also present some rigorous experiment showing the approach and some concrete result. 
Stefano Galatolo, Isaia Nisoli, Beno\^it Saussol
math.DS