Doubly intermittent maps with critical points, unbounded derivatives and regularly varying tail (Q6598513)

Maps with two intermittent fixed points and unbounded derivatives were studied by \textit{D. Coates} et al. [Commun. Math. Phys. 402, No. 2, 1845--1878 (2023; Zbl 1526.37042)].\N\NThe authors of the paper reviewed here extend results of [loc. cit.] by considering an overlapping class of maps \(\widehat{\mathfrak{G}}\) with regularly varying tails. They obtain their results by applying Karamata Theory and approaches similar to those of \textit{M. Holland} [Ergodic Theory Dyn. Syst. 25, No. 1, 133--159 (2005; Zbl 1073.37044)]. They show that all maps in \(\widehat{\mathfrak{G}}\) admit a unique invariant \(\sigma\)-finite measure equivalent to Lebesgue measure. Next they give the subclass \(\mathfrak{G}\) of \(\widehat{\mathfrak{G}}\) where all maps in \(\mathfrak{G}\) admit a unique ergodic invariant probability measure equivalent to Lebesgue measure. Furthermore, when this invariant measure is finite, they give a formula for the measure-theoretical entropy and a very slow upper bound for the decay of correlations.