Weak Gibbs measures for certain non-hyperbolic systems

We study a weak Gibbs property of equilibrium states for potentials of weak bounded variation and for maps admitting indifferent periodic points. We f urther establish statistical properties of the weak Gibbs measures and boun ds of their pointwise dimension. We apply our results to higher-dimensional maps (which are not necessarily conformal) with indifferent periodic point s and show that their absolutely continuous finite invariant measures are w eak Gibbs measures.