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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 513061, 14 pages
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.


We consider one family of 2-valued transformations on the interval [0, 1] with measure , endowed with a set of weight functions. We construct invariant measure for this multivalued dynamical system with weights and show the interplay between such systems and masked dynamical systems, which leads to image processing.