  We shall describe a new construction of equilibrium states for a class of
partially hyperbolic systems. This generalises our construction for Gibbs
measures in the uniformly hyperbolic setting. This more general setting
introduces new issues that we need to address carefully, in particular
requiring additional assumptions on the transformation. We treat two cases:
either the centre-stable manifold satisfies a bounded expansion condition; or
the centre-unstable manifold satisfies a subexponential contraction condition
which appears new in the context of equilibrium state constructions. The
problem of constructing equilibrium states was previously raised by Pesin-Sinai
and Dolgopyat for the particular case of u-Gibbs measures, and by Climenhaga,
Pesin and Zelerowicz for other equilibrium states.
