Is the process of finding f′ chaotic?
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 en...
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| Format: | Article |
| Language: | Spanish |
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Universidad Industrial de Santander
2004-09-01
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| Series: | Revista Integración |
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| Online Access: | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/510 |
| Summary: | 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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| ISSN: | 0120-419X 2145-8472 |