skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 1

Search for: All records

Creators/Authors contains: "TODD, MIKE"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Ergodic Theory and Dynamical Systems)
    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. 
    more » « less
    Free, publicly-accessible full text available December 1, 2026
  2. ; (, Ergodic Theory and Dynamical Systems)
    null (Ed.)
    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. 
    more » « less
    Full Text Available