3 citations · 6 across the 8 of their papers we have counts for
9 papers
Reduction theory for Fuchsian groups with cusps
Adam Abrams, Svetlana Katok, Ilie Ugarcovici
We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hype…
On the topological entropy of (a,b)-continued fraction transformations
Adam Abrams, Svetlana Katok, Ilie Ugarcovici
We study the topological entropy of a two-parameter family of maps related to (a,b)-continued fraction algorithms and prove that it is constant on a square within the parameter spa…
Destruction of CPE-normality along deterministic sequences
Adam Abrams, Tomasz Downarowicz
Let be a shift-invariant measure on , where is a finite or countable alphabet. We say that an infinite subset (where $s…
Rigidity and flexibility of entropies of boundary maps associated to Fuchsian groups
Adam Abrams, Svetlana Katok, Ilie Ugarcovici
Given a closed, orientable surface of constant negative curvature and genus , we study the topological entropy and measure-theoretic entropy (with respect to a smooth inva…
Rigidity of topological entropy of boundary maps associated to Fuchsian groups
Adam Abrams, Svetlana Katok, Ilie Ugarcovici
Given a closed, orientable surface of constant negative curvature and genus , we study a family of generalized Bowen-Series boundary maps and prove the following rigidity…
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…
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…
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…
Adler and Flatto revisited: cross-sections for geodesic flow on compact surfaces of constant negative curvature
Adam Abrams, Svetlana Katok
We describe a family of arithmetic cross-sections for geodesic flow on compact surfaces of constant negative curvature based on the study of generalized Bowen-Series boundary maps…