Asymptotic escape rates and limiting distributions for multimodal maps
Abstract
We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and Hölder potentials. For small holes, we show that a large class of initial distributions share the same escape rate and converge to a unique absolutely continuous conditionally invariant measure; we also prove a variational principle connecting the escape rate to the pressure on the survivor set, with no conditions on the placement of the hole. Finally, introducing a weak condition on the centre of the hole, we prove scaling limits for the escape rate for holes centred at both periodic and non-periodic points, as the diameter of the hole goes to zero.
Citation
Demers , M & Todd , M J 2021 , ' Asymptotic escape rates and limiting distributions for multimodal maps ' , Ergodic Theory and Dynamical Systems , vol. 41 , no. 6 , pp. 1656-1705 . https://doi.org/10.1017/etds.2020.14
Publication
Ergodic Theory and Dynamical Systems
Status
Peer reviewed
ISSN
0143-3857Type
Journal article
Rights
Copyright © The Author(s) 2020. Published by Cambridge University Press. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/etds.2020.14
Description
Funding: MD is partially supported by NSF grant DMS 1800321.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.