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SUMMARY:Counting loxodromics for hyperbolic actions - Samuel Taylor (Yale 
 University)
DTSTART:20170109T143000Z
DTEND:20170109T153000Z
UID:TALK69869@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Consider a nonelementary action by isometries of a hyperbolic 
 group G on a hyperbolic metric space X. Besides the action of G on its Cay
 ley graph\, some examples to bear in mind are actions of G on trees and qu
 asi-trees\, actions on nonelementary hyperbolic quotients of G\, or exampl
 es arising from naturally associated spaces\, like subgroups of the mappin
 g class group acting on the curve graph. <br> We show that the set of elem
 ents of G which act as loxodromic isometries of X (i.e those with sink-sou
 rce dynamics) is generic. That is\, for any finite generating set of G\, t
 he proportion of X-loxodromics in the ball of radius n about the identity 
 in G approaches 1 as n goes to infinity. We also establish several results
  about the behavior in X of the images of typical geodesic rays in G. For 
 example\, we prove that they make linear progress in X and converge to the
  boundary of X. This is joint work with I. Gekhtman and G. Tiozzo.
LOCATION:Seminar Room 1\, Newton Institute
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