Inducing Schemes with Finite Weighted Complexity.

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 φ + t ψ 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. Baladi and Demers (J Am Math Soc 33(2):381–449, 2020; J Mod Dyn 18:415–493, 2022) established general thermodynamic formalism for the Sinai dispersing billiards. As an application, our results provide an alternative proof for the existence, uniqueness and statistical properties of the equilibrium measures for the Sinai dispersing billiards with respect to the family of geometric potentials. [ABSTRACT FROM AUTHOR]