%0 Journal Article
%A Hughes, Bruce
%A Martínez Pérez, Álvaro
%A Morón, Manuel A.
%T Bounded distortion homeomorphisms on ultrametric spaces
%D 2010
%@ 1239-629X
%U https://hdl.handle.net/20.500.14352/42143
%X It is well-known that quasi-isometrics between R-trees induce power quasi-symmetric homeomorphisms between their ultrametric end spaces. This paper investigates power quasi-symmetric homeomorphisms between bounded, complete, uniformly perfect, ultrametric spaces (i.e., those ultrametric spaces arising up to similarity as the end spaces of bushy trees). A bounded distortion property is found that characterizes power quasi-symmetric homeomorphisms between such ultrametric spaces that are also pseudo-doubling. Moreover, examples are given showing the extent to which the power quasi-symmetry of homeomorphisms is not captured by the quasiconformal and bi-Holder conditions for this class of ultrametric spaces.
%~