Continuous maps on compact metric spaces are an important source of examples of measure-preserving transformations. In this chapter the basic properties of such maps are studied, and the ergodic decomposition is introduced. Equidistribution and generic orbits are introduced, and Furstenberg’s proof of Weyl’s equidsitrubution theorem for polynomials with an irrational coefficient is given.
KeywordsInvariant Measure Ergodic Theorem Invariant Probability Measure Ergodic Measure Unique Ergodicity
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