Abstract
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 language | English |
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Pages (from-to) | 367-424 |
Number of pages | 58 |
Journal | Israel Journal of Mathematics |
Volume | 221 |
Issue number | 1 |
Early online date | 11 Jul 2017 |
DOIs | |
Publication status | Published - Sept 2017 |
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Dive into the research topics of 'Equilibrium states, pressure and escape for multimodal maps with holes'. Together they form a unique fingerprint.Profiles
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Mike Todd
- School of Mathematics and Statistics - Deputy Head of School
- Pure Mathematics - Professor
Person: Academic