Slow escaping points of quasiregular mappings

摘要: This article concerns the iteration of quasiregular mappings on Rd and entire functions C. It is shown that there are always points at which iterates a map tend to infinity controlled rate. Moreover, an asymptotic rate escape result proved new even for transcendental functions. Let f:Rd→Rd be type. Using novel methods proof, we generalise results Rippon Stallard in complex dynamics show Julia set f contains fn arbitrarily slowly. We also prove that, any large R, point x with modulus approximately R such growth |fn(x)| iterated maximum Mn(R,f).