Uniformly refinable maps

Uniformly approachable maps∗

Throughout the paper we will use the standard definitions and notation ([ABR], [E]). Let X and Y be metric spaces. The goal is to study some intermediate classes of functions between the class Cuc(X,Y ) of all uniformly continuous mappings (briefly, UC) from X into Y and the class C(X,Y ) of all continuous functions f :X → Y . These classes, defined below, have been intensively studied in [BD] ...

Random Perturbations of Non-Uniformly Expanding Maps

Exponential Law for Uniformly Continuous Proper Maps

EXPONENTIAL LAW FOR UNIFORMLY CONTINUOUS PROPER MAPS R . AYALA, E . DOMINGUEZ, A . QUINTERO The purpose of this note is to prove the exponential law for uniformly continuous proper maps . Let X be a regular space and Y a locally compact regular space . It is well known that the spaces of continuousmaps C(X x Y, Z) and C(X, C(Y Z)) are homeomorphic considering the compact-open topology. This pro...

Random perturbations of non - uniformly expanding maps ∗

We give both sufficient conditions and necessary conditions for the stochastic stability of non-uniformly expanding maps either with or without critical sets. We also show that the number of probability measures describing the statistical asymptotic behaviour of random orbits is bounded by the number of SRB measures if the noise level is small enough. As an application of these results we prove...

Uniformly Quasiregular Maps with Toroidal Julia Sets

The iterates of a uniformly quasiregular map acting on a Riemannian manifold are quasiregular with a uniform bound on the dilatation. There is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We construct the first examples of uniformly quasiregular mappings that have a 2-torus as the Julia set. The spaces supporting this type of mappings incl...