Topological Entropy Of Periodic Coven Cellular Automata

Cellular automata was formally introduced by John von Neumann in 1951. In the mathematical literature, Hedlund established a connection between cellu-lar automata and symbolic dynamical systems in the first time in 1969. In recent decades, more and more researchers focus their attention on studying the theo-retical of cellular automata. As a discrete symbolic dynamical system, there are two very important topics:studying every point's trajectory and computing the system's topological entropy. This thesis is consist of five chapters.In Chapter 1, we present the origin, the development and applied aspects of cellular automata in this thesis. We also give the main results of this thesis.In Chapter 2, we recall some basic facts on dynamical systems and Ergodic theory.In Chapter 3, it is devoted to introduce some propositions of cellular automa-ta and establish an automata average as the ergodic average, and then we will prove that the automata average converges to spatial average.In Chapter 4, we investigate a class of nonlinear cellular automata-periodic Coven cellular automata, and prove that the topological entropy of Coven cellular automata is In 2 while the minimal period of the corresponding periodic word is greater than half of length of this word, and so it is Li-York chaotic. In addition, its maximal entropy measure is not unique.In Chapter 5, we discuss the topological entropy of other nonlinear cellular automatas.