Abstract
Skew products with ergodic automorphisms of compact abelian groups arise naturally in several contexts. For example, suppose S is an automorphism of the compact group G, and H is an S-invariant closed subgroup. By taking a measurable cross section to the quotient map G → G/H, the transformation S can be regarded as a skew product of the quotient automorphism SG/H with the restriction SH of S to H. We can study S by studying the simpler components, SG/H and SH, and how they are joined in a skew product. This method was used in proving that ergodic automorphisms of compact groups are measure theoretically isomorphic to Bernoulli shifts [3]. Crucial to this method is the result that if SH is ergodic, then the skew product S measure theoretically splits into the direct product SG/H × SH.
Supported in part by NSF Grant MCS77-04915
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© 1981 Springer Science+Business Media New York
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Lind, D.S. (1981). Finitarily Splitting Skew Products. In: Katok, A. (eds) Ergodic Theory and Dynamical Systems I. Progress in Mathematics, vol 10. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-6696-4_2
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DOI: https://doi.org/10.1007/978-1-4899-6696-4_2
Publisher Name: Birkhäuser, Boston, MA
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