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Golubencev A. F., Anikin V. M. Invariant subspaces for linear evolution operators of chaotic maps. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 1, pp. 3-17. DOI: 10.18500/0869-6632-2005-13-1-3-37

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Invariant subspaces for linear evolution operators of chaotic maps

Golubencev Aleksandr Fedorovich, Saratov State University
Anikin Valerij Mihajlovich, Saratov State University

Invariant functional subspaces for the Perron-Frobenius operator of a piece-wise linear chaotic Renyi map is constructed to find its first eigenfunctions.

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  1. Golubentsev AF, Anikin VM, Arkadaksky SS. On some properties of the Frobenius-Perron operator for Bernoulli shifts. Izvestiya VUZ. Applied Nonlinear Dynamics. 2000;8(2):67–73 (in Russian).
  2. Renyi A. Representation for real numbers and their ergodic properties. Acta. Math. Acad. Sc. Hungar. 1957;8(3–4):477–493. DOI: 10.1007/BF02020331.
  3. Rokhlin VA. Exact endomorphisms of the Lebesgue space. Izvestiya: Mathematics. 1961;25(4)499–530 (in Russian).
  4. Gelfond AO. On one general property of number systems. Izvestiya: Mathematics. 1959;23(6):800–814 (in Russian).
  5. Mori H, So BC, Ose T. Time-correlation functions of one-dimensional transformations. Progress of Theoretical Physics. 1981;66(4):1266–1283. DOI: 10.1143/PTP.66.1266.
  6. Anikin VM, Arkadaksky SS. Piecewise linear mappings with non-uniform invariant distribution. Radio Engineering. 2005;(4):78–85 (in Russian).
  7. Gantmacher FR. The Theory of Matrices. AMS Chelsea Publishing; 1959. 660 p.
  8. Okunev LY. Higher Algebra. Moscow: Prosveshcheniye; 1966. 336 p. (in Russian).
  9. Blank LM. Stability and Localization in Chaotic Dynamics. Moscow: MCCME; 2001. 352 p. (in Russian).
  10. Lasota A, Mackey MC. Probabilistic Properties of Deterministic Systems. Cambridge: Cambridge University Press; 1985. 360 p. DOI: 10.1017/CBO9780511897474.
  11. Iosifescu M, Kraaikamp C. Metrical Theory of Continued Fractions. Kluwer Boston Inc.; 2002. 346 p. DOI: 10.1007/978-94-015-9940-5.
  12. Korn G, Korn T. Handbook of Mathematics for Scientists and Engineers. Dover Publications; 2000. 1152 p.
  13. Schuster G. Deterministic Chaos. Wiley; 1995. 320 p.
  14. Anikin VM, Goloubentsev AF. Analysis of biological chaotic rythmes. In: Tuchin VV, editor. Proc. SPIE. Complex Dynamics, Fluctuations, Chaos, and Fractals in Biomedical Photonics. Vol. 5330. SPIE; 2004. P. 167–177.
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