3 papers
math.DS2020
Extremal parameters and their duals for Fuchsian boundary maps
Adam Abrams
We describe arithmetic cross-sections for geodesic flow on compact surfaces of constant negative curvature using generalized Bowen-Series boundary maps and their natural extensions…
math.DS2019
Finite partitions for several complex continued fraction algorithms
Adam Abrams
We present a property satisfied by a large variety of complex continued fraction algorithms (the "finite building property") and use it to explore the structure of bijectivity doma…
math.DS2019
Flexibility of measure-theoretic entropy of boundary maps associated to Fuchsian groups
Adam Abrams, Svetlana Katok, Ilie Ugarcovici
Given a closed, oriented, compact surface of constant negative curvature and genus , we study the measure-theoretic entropy of the Bowen-Series boundary map with respe…