Abstract
It has been long known that the pure death processes with proliferation can display a chaotic dynamics. In this paper we analyse long time dynamics of fragmentation processes which can be thought of as a generalization of death processes. In particular we show that, if combined with a proliferative process, their dynamics also can become chaotic.
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The author thanks the anonymous referees whose careful reading of the manuscript contributed to a significant improvement of the final version.
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The research was supported by the National Research Foundation of South Africa under grant GUN 2025057 and the University of KwaZulu-Natal Research Fund.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Banasiak, J. On an irregular dynamics of certain fragmentation semigroups. RACSAM 105, 361–377 (2011). https://doi.org/10.1007/s13398-011-0015-9
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DOI: https://doi.org/10.1007/s13398-011-0015-9
Keywords
- Fragmentation processes
- Death processes
- Long time behaviour
- Compact semigroups
- Analytic semigroups
- Chaotic semigroups