A non-trivial relation between some many-dimensional chaotic discrete dynamical systems and some one-dimensional chaotic discrete dynamical systems

Chaotic maps are very useful in practical applications. In this paper, we present a method for constructing the many-dimensional chaotic discrete dynamical systems using semiconjugacy property. The chaotic property in one dimension may be influenced the chaotic property in higher-dimensions. In fact, using the one-dimensional chaotic maps and semiconjugacy property, we construct some many-dimensional chaotic discrete dynamical systems. These systems may be used as random number generators in Monte Carlo simulations. Also, these systems may be used in practical applications such as chaotic cryptography and evolutionary algorithms.