Origination of the singular continuous spectrum in the conflict dynamical systems

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.

Full Text

Article Information

Title	Origination of the singular continuous spectrum in the conflict dynamical systems
Source	Methods Funct. Anal. Topology, Vol. 15 (2009), no. 1, 15-30
MathSciNet	MR2502635
Copyright	The Author(s) 2009 (CC BY-SA)

Authors Information

T. Karataieva
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

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

Citation Example

T. Karataieva and V. Koshmanenko, Origination of the singular continuous spectrum in the conflict dynamical systems, Methods Funct. Anal. Topology 15 (2009), no. 1, 15-30.

BibTex

@article {MFAT461,
    AUTHOR = {Karataieva, T. and Koshmanenko, V.},
     TITLE = {Origination of the singular continuous spectrum in the conflict dynamical systems},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {15},
      YEAR = {2009},
    NUMBER = {1},
     PAGES = {15-30},
      ISSN = {1029-3531},
  MRNUMBER = {MR2502635},
       URL = {http://mfat.imath.kiev.ua/article/?id=461},
}