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Point spectrum in conflict dynamical systems with fractal partition


Abstract

We discuss the spectral problem for limit distributions of conflict dynamical systems on spaces subjected to fractal divisions. Conditions ensuring the existence of the point spectrum are established in two cases, the repulsive and the attractive interactions between the opponents. A key demand is the strategy of priority in a single region.

Key words: Complex system, dynamical system, conflict interaction, dynamical system of conflict, stochastic vector, probability measure, fractal partition, iterated function system, self-similar and similar structure measure, point spectrum, approximation of singular distributions, weak convergence, Dirac delta-function.


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Article Information

TitlePoint spectrum in conflict dynamical systems with fractal partition
SourceMethods Funct. Anal. Topology, Vol. 25 (2019), no. 4, 324-338
MilestonesReceived 31/10/2019
CopyrightThe Author(s) 2019 (CC BY-SA)

Authors Information

V. Koshmanenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

O. Satur 
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

V. Voloshyna
Taras Shevchenko National University of Kyiv, 60 Volodymyrska, Kyiv, 01033, Ukraine;
University of Toulon, Avenue de l’Universite, 83130, La Garde, France

 


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Citation Example

V. Koshmanenko, O. Satur, and V. Voloshyna, Point spectrum in conflict dynamical systems with fractal partition, Methods Funct. Anal. Topology 25 (2019), no. 4, 324-338.


BibTex

@article {MFAT1241,
    AUTHOR = {V. Koshmanenko and O. Satur and V. Voloshyna},
     TITLE = {Point spectrum  in conflict dynamical systems with fractal partition},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {25},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {324-338},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=1241},
}


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