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Positivity

, Volume 10, Issue 1, pp 39–49 | Cite as

Spectral Properties of Image Measures Under the Infinite Conflict Interaction

  • Sergio Albeverio
  • Volodymyr Koshmanenko
  • Mykola Pratsiovytyi
  • Grygoriy Torbin
Article

Abstract

We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension.

Mathematics Subject Classification (2000)

11A67 11K55 26A46 28A80 28D05 60G30 

Keywords

Conflict interaction Hausdorff dimension image measure probability measure singular measure stochastic matrix 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  • Sergio Albeverio
    • 1
    • 2
    • 3
    • 4
    • 5
  • Volodymyr Koshmanenko
    • 6
  • Mykola Pratsiovytyi
    • 7
  • Grygoriy Torbin
    • 7
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnGermany
  2. 2.BiBos, Bielefeld-Bonn, Universität BielefeldBielefeldGermany
  3. 3.SFB-611, Universität BonnBonnGermany
  4. 4.IZKSBonnGermany
  5. 5.CERFIM Locarno and Acc. Arch. Locarno and USISwitzerland
  6. 6.Institute of MathematicsKyivUkraine
  7. 7.National Pedagogical UniversityKyivUkraine

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