Marc Kesseböhmer: Thermodynamic formalism for transient dynamics on the real line

We investigate ${\mathbb{R},+)$ extensions of certain interval maps and introduce the notion of fibre-induced pressure to generalise the idea of Gurevich pressure to skew-product dynamical systems. In this way we characterise recurrent potentials depending only on the base system in terms of the thermodynamic formalism. We study the Hausdorff dimension of the recurrent and transient set, and determine the multifractal decomposition spectrum with respect to the $\alpha$ -escaping sets. This provides a one-dimensional model for the phenomenon of dimension gaps analogous to limit sets of Kleinian groups.

(Joint work with Maik Gröger and Johannes Jaerisch)