Thermodynamical formalism associated with inducing schemes for one-dimensional maps

For a smooth map $f$ of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions $\varphi$ on I which admit a unique equilibrium measure $\mu_\varphi$. Our results apply to unimodal maps corresponding to a positive Lebesgue measure set of parameters in a one-parameter transverse family.