Is the process of finding f′ chaotic?

• Autores: Héctor Méndez Lango
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 22, Nº. 1-2, 2004, págs. 37-41
• Idioma: inglés
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• Resumen

  • Let (H (C) , ρ) be the metric space of all entire functions f where the metric ρ induces the topology of uniform convergence on compact subsets of the complex plane. Let D : H (C) → H (C) be the linear mapping that assigns to each f its derivative, D(f) = f′ . We show in this note that the set of entire functions that are periodic under this map is dense in (H (C) , ρ). It implies that D : H (C) → H (C) is chaotic in the sense of Devaney.

• Referencias bibliográficas
  • Citas [1]Banks J., Brooks J., Cairns G., Davis G.andStacey P.“On Devaney’sDefinition of Chaos”,American Mathematical Monthly,99(1992), 332–334.
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  • [3]Conway J. B.Functions of One Complex Variable I, Second Edition, Springer–Verlag, New York, 1978.
  • [4]Devaney R. L.An Introduction to Chaotic Dynamical Systems, Second Edition,Addison–Wesley, Redwood City, 1989.