On an irregular dynamics of certain fragmentation semigroups

Open Access
Original Paper

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.

Keywords

Fragmentation processes Death processes Long time behaviour Compact semigroups Analytic semigroups Chaotic semigroups 

Mathematics Subject Classification (2000)

47D06 

Notes

Acknowledgments

The author thanks the anonymous referees whose careful reading of the manuscript contributed to a significant improvement of the final version.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of KwaZulu-NatalDurbanSouth Africa
  2. 2.Institute of MathematicsTechnical University of ŁódźŁódźPoland

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