Non-expanding maps and Busemann functions
2001 (English)In: Ergodic Theory and Dynamical Systems, ISSN 0143-3857, E-ISSN 1469-4417, Vol. 21, 1447-1457 p.Article in journal (Refereed) Published
We give stronger versions and alternative simple proofs of some results of Beardon, [Be1] and [Be2]. These results concern contractions of locally compact metric spaces and generalize the theorems of Wolff and Denjoy about the iteration of a holomorphic map of the unit disk. In the case of unbounded orbits, there are two types of statements which can sometimes be proven; first, about invariant horoballs, and second, about the convergence of the iterates to a point on the boundary. A few further remarks of similar type are made concerning certain random products of sernicontractions and also concerning semicontractions of Gromov hyperbolic spaces.
Place, publisher, year, edition, pages
2001. Vol. 21, 1447-1457 p.
IdentifiersURN: urn:nbn:se:kth:diva-20996ISI: 000171413200009OAI: oai:DiVA.org:kth-20996DiVA: diva2:339693
QC 201005252010-08-102010-08-10Bibliographically approved