Artículo Original
Publicado 2004-09-16
Palabras clave
- Entire functions,
- chaotic maps
Cómo citar
Méndez-Lango, H. (2004). Is the process of finding f′ chaotic?. Revista Integración, Temas De matemáticas, 22(1 y 2), 37–41. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/510
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.
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Referencias
[1]Banks J., Brooks J., Cairns G., Davis G.andStacey P.“On Devaney’sDefinition of Chaos”,American Mathematical Monthly,99(1992), 332–334.
[2]Blair C.andRubel L. A.“A Universal Entire Function”,American Mathema-tical Monthly,90(1983), 331–332.
[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.
[2]Blair C.andRubel L. A.“A Universal Entire Function”,American Mathema-tical Monthly,90(1983), 331–332.
[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.