# Inducing Schemes with Finite Weighted Complexity

## TL;DR

This paper develops a thermodynamic formalism for certain dynamical systems with inducing schemes under finite weighted complexity, showing liftability of measures with large pressure when a compatible partition exists.

## Contribution

It introduces a thermodynamic formalism for systems with inducing schemes under finite weighted complexity and establishes liftability of measures with large pressure.

## Key findings

- Thermodynamic formalism established for systems with inducing schemes.
- Liftability of ergodic measures with large pressure under certain conditions.
- Conditions under which the formalism applies are specified.

## 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 $\varphi+t\psi$ 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.