From set-valued dynamical processes to fractals

• Autorzy: Guzik Grzegorz , Kleszcz Grzegorz

Identyfikatory

DOI

10.7494/OpMath.2025.45.5.601

• Języki publikacji: EN

Abstrakty

EN

We present a general theory of topological semiattractors and attractors for set-valued semigroups. Our results extend and unify those previously obtained by Lasota and Myjak. In particular, we naturally generalize the concept of semifractals for the systems acting on Hausdorff topological spaces. The main tool in our analysis is the notion of topological (Kuratowski) limits. We especially focus on the forward asymptotic behavior of discrete set-valued processes generated by sequences of iterated function systems. In this context, we establish sufficient conditions for the existence of fractal-type limit sets.

Słowa kluczowe

EN

topological limit; lower semicontinuous multifunction; iterated function system; set-valued process; attractor

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2025
• Tom: Vol. 45, no. 5
• Strony: 601--621
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Guzik Grzegorz

• AGH University of Krakow, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30–059 Kraków, Poland

• https://orcid.org/0000-0002-6099-9499

autor

Kleszcz Grzegorz

• AGH University of Krakow, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30–059 Kraków, Poland

• https://orcid.org/0000-0003-3044-5097

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)