Periodic domains of quasiregular mapsTools Nicks, Daniel A. and Sixsmith, David J. (2016) Periodic domains of quasiregular maps. Ergodic Theory and Dynamical Systems . ISSN 14694417 (In Press)
AbstractWe consider the iteration of quasiregular maps of transcendental type from Rd to Rd. We give a bound on the rate at which the iterates of such a map can escape to infinity in a periodic component of the quasiFatou set. We give examples which show that this result is best possible. Under an additional hypothesis, which is satisfied by all uniformly quasiregular maps, this bound can be improved to be the same as those in a Baker domain of a transcendental entire function.
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