Diffusion to infinity for periodic orbits in meromorphic dynamics
Volume 174 / 2002
Fundamenta Mathematicae 174 (2002), 263-269
MSC: Primary 37F10, 37F45; Secondary 30D05, 32H50.
DOI: 10.4064/fm174-3-6
Abstract
A small perturbation of a rational function causes only a small perturbation of its periodic orbits. We show that the situation is different for transcendental maps. Namely, orbits may escape to infinity under small perturbations of parameters. We show examples where this “diffusion to infinity” occurs and prove certain conditions under which it does not.
