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