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We show an elementary method to have (finite time and asymptotic) computerassisted explicit upper bounds on convergence to equilibrium (decay ofcorrelations) and escape rate for systems satisfying a Lasota Yorke inequality.The bounds are deduced by the ones of suitable approximations of the system'stransfer operator. We also present some rigorous experiment showing theapproach and some concrete result.

An elementary way to rigorously estimate convergence to equilibrium and escape rates