Equivalence of cocycles under an irrational rotation

Authors:
Larry Baggett and Kathy Merrill

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

MSC:
Primary 28D05; Secondary 42A05, 58F11

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

MathSciNet review:
948146

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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 . 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.

**[1]**L. Baggett and K. Merrill,*Representations of the Mautner group and cocycles of an irrational rotation*, Michigan Math. J.**33**(1986), 221-229. MR**837580 (87h:22011)****[2]**H. Helson,*Analyticity on compact abelian groups*, Algebras In Analysis, Academic Press, (1975), pp. 1-62. MR**0427959 (55:989)****[3]**K. Merrill,*Cohomology of step functions under irrational rotations*, Israel J Math.**52**(1985), pp. 320-340. MR**829362 (88b:39009)****[4]**C. C. Moore and K. Schmidt,*Coboundaries and homomorphisms for nonsingular actions and a problem of H. Helson*, Proc. London Math. Soc.**40**(1980), 443-475. MR**572015 (82a:22007)****[5]**K. Petersen,*On a series of cosecants related to a problem in ergodic theory*, Compositio Math.**26**(1973), 313-317. MR**0325927 (48:4273)****[6]**M. Stewart,*Irregularities of uniform distribution*, Acta Math. Sci. Hungar.**37**(1981), 185-221. MR**616890 (82k:10072)****[7]**W. A. Veech,*Strict ergodicity in zero-dimensional dynamical systems and the Kronecker-Weyl theorem*, , Trans. Amer. Math. Soc.**140**(1969), 1-33. MR**0240056 (39:1410)****[8]**-,*Finite group extensions of irrational rotations*, Israel J. Math.**21**(1975), 240-259. MR**0396913 (53:773)**

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

Article copyright:
© Copyright 1988
American Mathematical Society