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

Abstract

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