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: "Pfaff, Catherine"

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. ; (, Geometriae Dedicata)
    Inspired by results of Eskin and Mirzakhani (J Mod Dyn 5(1):71–105, 2011) counting closed geodesics of length at most L in the moduli space of a fixed closed surface, we consider a similar question in the Out(Fr) setting. The Eskin-Mirzakhani result can be equivalently stated in terms of counting the number of conjugacy classes (within the mapping class group) of pseudo-Anosovs whose dilatations have natural logarithm at most L. Let N(L) denote the number of Out(Fr)-conjugacy classes of fully irreducibles satisfying that the natural logarithm of their dilatation is at most L. We prove for r>2 that as L goes to infinity, the number N(L) has double exponential (in L) lower and upper bounds. These bounds reveal behavior not present in the surface setting or in classical hyperbolic dynamical systems. 
    more » « less
    Full Text Available 
  2. ; ; ; (, Transactions of the American Mathematical Society)
    Full Text Available 
  3. ; ; ; (, Geometry & Topology)
    Full Text Available 
  4. ; ; (, International Mathematics Research Notices)
    Abstract In this article, we propose an Outer space analog for the principal stratum of the unit tangent bundle to the Teichmüller space $${\mathcal{T}}(S)$$ of a closed hyperbolic surface $$S$$. More specifically, we focus on properties of the geodesics in Teichmüller space determined by the principal stratum. We show that the analogous Outer space “principal” periodic geodesics share certain stability properties with the principal stratum geodesics of Teichmüller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichmüller space context. 
    more » « less
    Full Text Available 
  5. ; (, International Journal of Algebra and Computation)
    Full Text Available