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Abstract and Applied Analysis
Volume 2014, Article ID 513061, 14 pages
http://dx.doi.org/10.1155/2014/513061
Research Article

On One 2-Valued Transformation: Its Invariant Measure and Application to Masked Dynamical Systems

Institute of Mathematics and Mechanics, Kazan Federal University, 18 Kremlyovskaya Street, Kazan 420008, Russia

Received 1 September 2014; Accepted 18 September 2014; Published 19 November 2014

Academic Editor: Adrian Petrusel

Copyright © 2014 P. I. Troshin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. I. Troshin, “Multivalued dynamical systems with weights,” Russian Mathematics, vol. 53, no. 7, pp. 28–42, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  2. P. I. Troshin, “On measure invariance for a 2-valued transformation,” Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, vol. 151, no. 4, pp. 183–191, 2009, http://arxiv-web3.library.cornell.edu/abs/0912.2210?context=math.NT. View at Google Scholar
  3. A. Rényi, “Representations for real numbers and their ergodic properties,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 8, pp. 477–493, 1957. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. W. Parry, “On the β-expansions of real numbers,” Acta Mathematica Academiae Scientiarum Hungaricae, vol. 11, pp. 401–416, 1960. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. B. Igudesman, “Top addresses for a certain family of iterated function system on a segment,” Russian Mathematics (Izvestiya VUZ. Matematika), vol. 53, no. 9, pp. 67–72, 2009. View at Google Scholar
  6. P. I. Troshin, “Code structure for Pairs of linear maps with some open problems,” in Frontiers in the Study of Chaotic Dynamical Systems with Open Problems, vol. 16 of World Scientific Series on Nonlinear Science: Series B, pp. 175–194, 2011. View at Google Scholar
  7. M. F. Barnsley, B. Harding, and K. Igudesman, “How to transform and filter images using iterated function systems,” SIAM Journal on Imaging Sciences, vol. 4, no. 4, pp. 1001–1028, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. M. F. Barnsley, “Theory and application of fractal tops,” in Fractals in Engineering: New Trends in Theory and Applications, pp. 3–20, Springer, London, UK, 2005. View at Google Scholar