Invariant Measures for Continuous Maps

Manfred Einsiedler () and Thomas Ward ()
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Manfred Einsiedler: ETH Zurich, Departement Mathematik
Thomas Ward: University of East Anglia, School of Mathematics

Chapter Chapter 4 in Ergodic Theory, 2011, pp 97-119 from Springer

Abstract: Abstract 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.

Keywords: Invariant Measure; Ergodic Theorem; Invariant Probability Measure; Ergodic Measure; Unique Ergodicity (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-85729-021-2_4

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DOI: 10.1007/978-0-85729-021-2_4

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