Sarah Bailey's Research Page

My current research is in the area of symbolic dynamics and ergodic theory under the direction of Karl Petersen. In partiuclar, I am studying Bratteli-Vershik systems. The space X is the space of infinite paths on a Bratteli diagram, and a Vershik (adic) transformation maps X to X. All Cantor minimal systems can be described by such a system, and much is known in this case. I am interested in extending some of these results to non-minimal systems. I'm interested in a particular family of such systems for which the number of vertices grows linearly, and the transformation is not continuous on a countable set. The most famous example of one of these systems in the Pascal adic. I am investigating these systems from both topological and measure-theoretic viewpoints. Part of my current research involves investigating orbit equivalence of two such systems and the relation with the dimension group invariant.

Publications
Ergodicity of the Euler adic transformation on the Euler graph, with Mike Keane, Karl Petersen and Ibrahim Salama
to appear: Math. Proc. Camb. Phil. Soc.
Random permutations and unique fully supported ergodicity for the Euler adic transformation, with Karl Petersen
submitted
 

 

 

Some Recent Presentations
Dynamical Properties of some non-stationary, non-simple Bratteli-Vershik systems (Poster)
AWM Workshop Poster Session, Joint Meetings, January 2006
San Antonio, TX
 
A General Family of Non-Stationary Non-Simple Bratteli-Vershik Systems
Ergodic Theory and Topological Dyanmics Seminar, November 2005
Wesleyan University, Middletown, CT
 
Dimension Groups for a family of non-simple Adic Transformantion
AMS Special Session on Measurable, Symbolic, and Tiling Dynamical Systems, October 2005
Annandale-on-Hudson, NY
 
Dynamical Properties of the Euler Adic Transformation
The Northwest Dynamics Symposium, August 2005
Victoria, Canada
 
Non-Stationary Adic Transformations
The Visegrad Conference Dynamical Systems, July 2005
Prague, Czech Republic
 
Dynamical Properties of the Euler Adic
The Erwin Schrodinger International Institute for Mathematical Physics , June 2005
Vienna, Austria
 
The Euler Adic is Totally Ergodic and Loosely Bernoulli
Carolina Dynamics Conference, April 2005
Chapel Hill, NC
 
Computing dimension groups for a certain family of non-simple Bratteli diagrams
Maryland-Penn State Workshop on Dynmaical Systems, March 2005
College Park, Maryland
 
Uniqueness of the Symmetric Measure
Graduate Math Association Seminar, February 2005
Chapel Hill, NC
 
The Symmetric Measure of the Adic Transformation on the Euler Graph
Ergodic Theory and Dynamical Systems Seminar, February 2005
Chapel Hill, NC
 
Bratteli-Vershik Systems Associated to Positive Integer Polynomials
The Erwin Schrodinger International Institute for Mathematical Physics , May 2004
Vienna, Austria