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
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
Title
Point spectrum in conflict dynamical systems with fractal partition
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
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},
}
