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This note is concerned with approximation of dynamical indicators aspressures, Lyapunov exponents and dimension-like quantities, in systems withnonuniformly hyperbolic behavior. For this we let $P^*(\Phi) :=\sup_{\mu}\{h(\mu) + \mu(\Phi)\}$ be a variational pressure defined over asuitable class of Borel measurable potentials and prove that, for regularnonuniformly hyperbolic systems, $P^*(\Phi) = \sup_{\Omega}P^*(f|\Omega,\Phi)$,supremum taken over the family of $f$-invariant uniformly hyperbolic basicsets. We then apply this variational principle to the approximation ofdynamical indicators by horseshoes.

Variational principles and approximation of dynamical indicators for systems with nonuniformly hyperbolic behavior