Size of the set of attractors for iterated function systems
| Autor: | Adam Kwela, Paweł Klinga, Marcin Staniszewski |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems General Mathematics Applied Mathematics General Physics and Astronomy Statistical and Nonlinear Physics 01 natural sciences Measure (mathematics) 010305 fluids & plasmas Nonlinear Sciences::Chaotic Dynamics Set (abstract data type) Metric space Iterated function system 0103 physical sciences Attractor 010301 acoustics Mathematics |
| Zdroj: | Chaos, Solitons & Fractals. 128:104-107 |
| ISSN: | 0960-0779 |
| DOI: | 10.1016/j.chaos.2019.07.028 |
| Popis: | We discuss the smallness of the set of attractors for iterated function systems. This paper is an attempt to measure the difference between the family of IFS attractors and a broader family, the set of attractors for the weak iterated function systems. We prove that the IFS attractors form a σ-porous subset of K([0, 1]d), the family of compact subsets of a metric space [0, 1]d. We also show that weak IFS attractors form a first category set. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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