Asymptotic escape rates and limiting distributions for multimodal maps
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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.
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
Ergodic Theory and Dynamical Systems
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
DescriptionFunding: MD is partially supported by NSF grant DMS 1800321.
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