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Diffusion to infinity for periodic orbits in meromorphic dynamics

Janina Kotus, Grzegorz Świątek (2002)

Fundamenta Mathematicae

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.

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