Equilibrium states, pressure and escape for multimodal maps with holes

Mark F. Demers, Mike Todd

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


For a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant conditionally invariant measures and equilibrium states and prove a relation between the rate of escape and pressure with respect to these potentials. As a consequence, we obtain a Bowen formula: we express the Hausdorff dimension of the set of points which never exit through the hole in terms of the relevant pressure function. Finally, we obtain an expression for the derivative of the escape rate in the zero-hole limit.
Original languageEnglish
Pages (from-to)367-424
Number of pages58
JournalIsrael Journal of Mathematics
Issue number1
Early online date11 Jul 2017
Publication statusPublished - Sept 2017


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