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Let f be a (C^{1+alpha }) diffeomorphism of a compact Riemannian manifold and (mu  an ergodic hyperbolic measure with positive entropy. We prove that for every continuous potential (phi  there exists a sequence of basic sets (Omega _n) such that the topological pressure (P(f|Omega _n,phi )) converges to the free energy (P_{mu }(phi ) = h(mu ) + int phi {dmu }). We also prove that for a suitable class of potentials (phi  there exists a sequence of basic sets (Omega _n) such that (P(f|Omega _n,phi ) rightarrow P(phi )).

On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior