Yang, Chaos Caused by a Topologically Mixing Map, in Dynamical Systems and Related Topics ( World Scientific, Singapore, 1992 ). to the direct product of a Bernoulli shift by a zero entropy system splits in the same way. Wolfram, A New Kind of Science ( Wolfram Media, Champaign, Illinois, USA, 2002 ). Extender sets and measures of maximal entropy for subshifts. Wolfram, Theory and Application of Cellular Automata ( World Scientific, Singapore, 1986 ). We make the set shift invariant by taking the original sets. by Kolmogorov in 1958-59 of the concept of entropy as an invariant for measure-preserving transformation. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos ( Springer-Verlag, Berlin, NY, 1990 ). Our basic example will not satisfy this, as it is much easier to build zero entropy subshifts. entropy of the decimal expansion transformation and the Bernoulli shift. Ohi, Chaotic properties of the elementary cellular automata rule 168 in Wolfram's class I, AUTOMATA-2008: Theory and Applications of Cellular Automata ( Luniver Press, UK, 2008 ). Baba, Introduction to Chaos ( Institute of Physics Publishing, Bristol, 1999 ). Entropy is a nontrivial invariant that, said simply, measures the exponential growth rate of the number of orbits. Kitchens, Symbolic Dynamics: One-Sided, Two-Sided and Countable State Markov Shifts ( Springer-Verlag, Berlin, NY, 1998 ). für die reine und Angewandte Mathematik 547, 51 (2002).
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