Transience and thermodynamic formalism for infinitely branched interval maps (Q2909047)

This paper studies the thermodynamic formalism of a certain parameterized family of countably piecewise linear maps \(F_\lambda:(0,1] \rightarrow (0,1]\) which was introduced by S. van Strien and examined by \textit{B. Stratmann} and \textit{R. Vogt} [Nonlinearity 10, No. 2, 565--577 (1997; Zbl 0909.28005)]. The authors obtain the parameters for which \(F_\lambda\) has an acip, define and find the conformal pressure for \(F_\lambda\), study the topological pressure on compact invariant sets, and calculate the Hausdorff dimensions of the hyperbolic and escaping sets. They connect the results to the concepts of transience and recurrence proposed by \textit{O. Sarig} [Isr. J. Math. 121, 285--311 (2001; Zbl 0992.37025)] for countable Markov shifts.