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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 $ϕ$ on I which admit a unique equilibrium measure $μ_ϕ$. Our results apply to unimodal maps corresponding to a positive Lebesgue measure set of parameters in a one-parameter transverse family.