Abstract

This work studies thermodynamic formalism for interval maps, focusing on Gibbs states, conformal measures, exponential mixing, and the spectral gap of the transfer operator. The main results show that, under suitable hypotheses, an exponentially mixing Gibbs state is unique and is equivalent to a unique non-atomic conformal measure. The appendix extends these ideas to intermittent maps, emphasizing the role of conformal measures in non-uniformly expanding dynamics