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Abstract We consider the initial‐value problem for a one‐dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we prove that the local energy decays exponentially fast in time, and provide the explicit constant to which the solution converges. The key ingredient of the proof is a high‐frequency resolvent estimate for an associated Helmholtz operator with a BV potential.
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This content will become publicly available on December 1, 2026
A trichotomy for hitting times and escape rates for a class of unimodal maps
Abstract We consider local escape rates and hitting time statistics for unimodal interval maps of Misiurewicz–Thurston type. We prove that for any pointzin the interval, there is a local escape rate and hitting time statistics that is one of three types. While it is key that we cover all pointsz, the particular interest here is whenzis periodic and in the postcritical orbit that yields the third part of the trichotomy. We also prove generalized asymptotic escape rates of the form first shown by Bruin, Demers and Todd.
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- PAR ID:
- 10654576
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Ergodic Theory and Dynamical Systems
- Volume:
- 45
- Issue:
- 12
- ISSN:
- 0143-3857
- Page Range / eLocation ID:
- 3663 to 3697
- Subject(s) / Keyword(s):
- hitting times, escape rate, unimodal maps, Misiurewicz–Thurston maps, inducing techniques
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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