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2024 | OriginalPaper | Chapter

Sequences of Uncountable Iterated Function Systems: The Convergence of the Sequences of Fractals and Fractal Measures Associated

Authors : Ion Mierlus-Mazilu, Lucian Nită

Published in: Mathematical Methods for Engineering Applications

Publisher: Springer Nature Switzerland

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Abstract

In this paper, we consider a sequence of uncountable iterated function system (U.I.F.S.). Each term of this sequence is built using an uncountable family of contractions and a linear and continuous operator. For each U.I.F.S. of the sequence we have an associated attractor, a Markov-type operator and a fractal measure.
We study the convergence of the corresponding attractors and fractal measures sequences.

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previous chapter Some Identities for Balancing and Lucas-Balancing Numbers in Bidimensional Version
next chapter Method of Hydrodynamic Images and Quantum Calculus in Fock-Bargmann Representation of Quantum States
Literature
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Chitescu, I., Ioana, L., Miculescu, R., Nita, L.: Sesquiliniar uniform vector integral. Proc. Indian Acad. Sci. (Math. Sci.) 125(2), 229–236 (2015)
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Chitescu, I., Ioana, L., Miculescu, R., Nita, L.: Monge-Kantorovich norms on spaces of vector measures. Results Math. 70, 349–371 (2016)MathSciNetCrossRef
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Chitescu, I.: Spatii de Functii (in Romanian). Editura Stiintifica si Enciclopedica, Bucharest (1983)
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Nita, L.: The attractor and the Hutchinson measure for an uncountable iterated function system. In: Proceedings of Mathematics and Educational Symposium of Department of Mathematics and Computer Science, Bucharest, 2nd edn., pp. 109–111 (2016)
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Siretchi, G.: Spatii Concrete in Analiza Functionala (in Romanian). Centrul de Multiplicare al Universitatii Bucuresti, Bucharest (1982)
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Constantinescu, S., Mierlus-Mazilu, I., Nita, L.: Families of iterated function systems. Convergences properties of the associated attractors and fractal measures. U.P.B. Sci. Bull. Ser. A 84(2), 107–115 (2022)
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D’Aniello, E., Steele, T.H.: Attractors for classes of iterated function systems. Eur. J. Math. 5(1), 116–137 (2019)MathSciNetCrossRef
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Mihail, A.: Recurrent iterated function systems. Rev. Roumaine Math. Pures Appl. 53(1), 43–53 (2008)MathSciNet
Metadata
Title
Sequences of Uncountable Iterated Function Systems: The Convergence of the Sequences of Fractals and Fractal Measures Associated
Authors
Ion Mierlus-Mazilu
Lucian Nită
Copyright Year
2024
Book
Mathematical Methods for Engineering Applications

Print ISBN: 978-3-031-49217-4

Electronic ISBN: 978-3-031-49218-1

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-49218-1_4

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