Origination of the singular continuous spectrum in the conflict dynamical systems

Authors

  • T. Karataieva Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine
  • V. D. Koshmanenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine  https://orcid.org/0000-0003-0411-4059

DOI:

Keywords:

Abstract

We study the spectral properties of the limiting measures in the conflict dynamical systems modeling the alternative interaction between opponents. It has been established that typical trajectories of such systems converge to the invariant mutually singular measures. We show that "almost always" the limiting measures are purely singular continuous. Besides we find the conditions under which the limiting measures belong to one of the spectral type: pure singular continuous, pure point, or pure absolutely continuous.

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Published

2009-03-25

Issue

Vol. 15 No. 1 (2009)

Section

Articles

How to Cite

Karataieva, T., and V. D. Koshmanenko. “Origination of the Singular Continuous Spectrum in the Conflict Dynamical Systems”. Methods of Functional Analysis and Topology, vol. 15, no. 1, Mar. 2009, pp. 15-30, https://zen.imath.kiev.ua/index.php/mfat/article/view/405.