Inducing Schemes with Finite Weighted Complexity

Abstract

In this paper, we consider a Borel 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 $\phi +t\psi$ 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.