Equivalence of cocycles under an irrational rotation

Baggett, Larry; Merrill, Kathy

doi:10.1090/S0002-9939-1988-0948146-8

Equivalence of cocycles under an irrational rotation
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by Larry Baggett and Kathy Merrill

Proc. Amer. Math. Soc. 104 (1988), 1050-1053

DOI: https://doi.org/10.1090/S0002-9939-1988-0948146-8

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Abstract:

This paper describes a method for studying the equivalence relation among cocycles for an irrational rotation. A parameterized family of cocycles is presented, which meets the equivalence class of each piecewise absolutely continuous function whose derivative is ${L^2}$. The difficulties in describing the equivalence among the elements of this family is shown to reduce to the analogous problem for describing equivalence among step functions, thereby relating this paper to the earlier work of Veech, Petersen, Merrill, and others.

References

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