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Let $f$ be a $C^{1+\alpha}$ nonuniformly hyperbolic diffeomorphism. We use aa nonadditive version of the topological pressure of a class of admissible,possibly noncontinuous potentials $P^*(\Phi)$ to prove the followingvariational equation: $P^*(\Phi) = \sup_{\Omega \in {\mathcalH}}P^*(f|\Omega,\Phi)$ supremum taken over the set ${\mathcal H}$ of basicsubsets in $M$. As a consequence we find a lower bound for the Cantor dimensionof the stable and unstable Cantor sets of a non trivial conformal nonuniformlyhyperbolic isolated sets.

A variational principle for systems with nonuniformly hyperbolic behavior with applications to the dimension theory