Symbolic Names and Generators
Consider a dynamical system, and let Q = {Q1, ..., Qk} be a partition of X into k measurable pair-wise disjoint pieces. Given a point x ∈ X, clearly x belongs to only one of the Qi. Similarly, the iterated point Tnx can belong to only one of the parts as well. The symbolic name of x, with regards to the partition Q, is the sequence of integers {an} such that
The set of symbolic names with respect to a partition is called the symbolic dynamics of the dynamical system. A partition Q is called a generator or generating partition if μ-almost every point x has a unique symbolic name.
Read more about this topic: Measure-preserving Dynamical System
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