13 citations · 96 across the 16 of their papers we have counts for
16 papers
Singularity of Cannon-Thurston maps
Vaibhav Gadre, Joseph Maher, Catherine Pfaff +1
In a closed fibered hyperbolic 3-manifold M ,the inclusion of a fiber S, with S and M lifted to the universal covers, gives an exponentially distorted embedding of the hyperbolic p…
Depth of free-by-cyclic groups
Spencer Dowdall, Yassine Guerch, Radhika Gupta +2
For a free group automorphism, we prove that its poset of attracting lamination orbits is a canonical invariant of the associated mapping torus. That is, if a free-by-cyclic group…
Quasi-geodesics in the Cannon-Thurston metric
Vaibhav Gadre, Joseph Maher, Catherine Pfaff +1
A closed fibered 3-manifold admits a complete hyperbolic metric if and only if it has a fibration with a pseudo-Anosov monodromy. The stable and the unstable laminations associated…
Bounded projections to the -factor graph
Matt Clay, Caglar Uyanik
Suppose is a free product , where each of the groups is torsion-free and is a free group of rank . Let be the de…
Random walk speed is a proper function on Teichmüller space
Aitor Azemar, Vaibhav Gadre, Sébastien Gouëzel +3
Consider a closed surface with negative Euler characteristic, and an admissible probability measure on the fundamental group of with finite first moment. Corresponding to e…
Slope Gap Distribution of Saddle Connections on the 2n-gon
Jonah Berman, Taylor McAdam, Ananth Miller-Murthy +2
We explicitly compute the limiting slope gap distribution for saddle connections on any 2n-gon. Our calculations show that the slope gap distribution for a translation surface is n…
Atoroidal dynamics of subgroups of Out(F_N)
Matt Clay, Caglar Uyanik
We show that for any subgroup of Out(), either contains an atoroidal element or a finite index subgroup of fixes a nontrivial conjugacy class in . This r…
Length functions on currents and applications to dynamics and counting
Viveka Erlandsson, Caglar Uyanik
The aim of this (mostly expository) article is twofold. We first explore a variety of length functions on the space of currents, and we survey recent work regarding applications of…
Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension
Hamid Al-Saqban, Paul Apisa, Alena Erchenko +3
We prove that for every flat surface , the Hausdorff dimension of the set of directions in which Teichmüller geodesics starting from exhibit a definite amount of deviation f…
Hyperbolic extensions of free groups from atoroidal ping-pong
Caglar Uyanik
We prove that all atoroidal automorphisms of act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new…
Simultaneous construction of hyperbolic isometries
Matt Clay, Caglar Uyanik
Given isometric actions by a group G on finitely many δ-hyperbolic metric spaces, we provide a sufficient condition that guarantees the existence of a single element in G that is h…
Perron-Frobenius theory and frequency convergence for reducible substitutions
Martin Lustig, Caglar Uyanik
We prove a general version of the classical Perron-Frobenius convergence property for reducible matrices. We then apply this result to reducible substitutions and use it to produce…
North-South dynamics of hyperbolic free group automorphisms on the space of currents
Martin Lustig, Caglar Uyanik
Let be a hyperbolic outer automorphism of a non-abelian free group such that and admit absolute train track representatives. We prove that acts on the sp…
The distribution of gaps for saddle connections on the octagon
Caglar Uyanik, Grace Work
We explicitly compute the limiting gap distribution for slopes of saddle connections on the flat surface associated to the regular octagon with opposite sides identified. This is t…
Dynamics of hyperbolic iwips
Caglar Uyanik
We present two proofs of the fact, originally due to Reiner Martin, that any fully irreducible hyperbolic element of acts on the projectivized space of geodesic currents…
Generalized north-south dynamics on the space of geodesic currents
Caglar Uyanik
We prove uniform north-south dynamics type results for the action of on the space of projectivized geodesic currents , wh…