We consider a measurable map of a compact metric space which admits an inducing scheme. Under the finite weighted complexity condition, we establish a thermodynamic formalism for a parameter family of potentials $\varphi+t\psi$ in an interval containing $t=0$.  Furthermore, if there is a generating partition compatible to the inducing scheme, we show that all ergodic invariant measures with sufficiently large pressure are liftable. Our results are applicable to the Sinai dispersing billiards with finite horizon, that is, we establish the equilibrium measures for the family of geometric potentials in a slightly restricted class. This is a joint work with Fang Wang and Hong-Kun Zhang.

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