Diffusion to infinity for periodic orbits in meromorphic dynamics

Tom 174 / 2002

Janina Kotus, Grzegorz Świątek Fundamenta Mathematicae 174 (2002), 263-269 MSC: Primary 37F10, 37F45; Secondary 30D05, 32H50. DOI: 10.4064/fm174-3-6

Streszczenie

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.

Autorzy

  • Janina KotusDepartment of Mathematics
    Warsaw University of Technology
    00-661 Warszawa, Poland
    e-mail
  • Grzegorz ŚwiątekDepartment of Mathematics
    Penn State University
    University Park, PA 16802, U.S.A.
    e-mail

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