# BV coboundaries over irrational rotations

Studia Mathematica (1997)

- Volume: 126, Issue: 3, page 253-271
- ISSN: 0039-3223

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topVolný, Dalibor. "BV coboundaries over irrational rotations." Studia Mathematica 126.3 (1997): 253-271. <http://eudml.org/doc/216454>.

@article{Volný1997,

abstract = {For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.},

author = {Volný, Dalibor},

journal = {Studia Mathematica},

keywords = {skew product; Anzei cocycle; coboundary},

language = {eng},

number = {3},

pages = {253-271},

title = {BV coboundaries over irrational rotations},

url = {http://eudml.org/doc/216454},

volume = {126},

year = {1997},

}

TY - JOUR

AU - Volný, Dalibor

TI - BV coboundaries over irrational rotations

JO - Studia Mathematica

PY - 1997

VL - 126

IS - 3

SP - 253

EP - 271

AB - For every irrational rotation we construct a coboundary which is continuous except at a single point where it has a jump, is nondecreasing, and has zero derivative almost everywhere.

LA - eng

KW - skew product; Anzei cocycle; coboundary

UR - http://eudml.org/doc/216454

ER -

## References

top- [1] W. Bułatek, M. Lemańczyk and D. Rudolph, Constructions of cocycles over irrational rotations, Studia Math. 125 (1997), 1-11. Zbl0891.28011
- [2] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 89 (1961), 573-601. Zbl0178.38404
- [3] P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Mém. Soc. Math. France 47 (1991). Zbl0754.28011
- [4] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95. Zbl0786.28011
- [5] A. Ya. Khintchine, Continued Fractions, Noordhoff, Groningen, 1963.
- [6] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
- [7] M. Lemańczyk, F. Parreau and D. Volný, Ergodic properties of real cocycles and pseudo-homogeneous Banach spaces, Trans. Amer. Math. Soc., to appear. Zbl0876.28021
- [8] W. Parry and S. Tuncel, Classification Problems in Ergodic Theory, London Math. Soc. Lecture Note Ser. 67, Cambridge Univ. Press, Cambridge, 1982. Zbl0487.28014
- [9] K. Schmidt, Cocycles of Ergodic Transformation Groups, Macmillan Lectures in Math. 1, Macmillan of India, 1977.
- [10] D. Volný, Cohomology of Lipschitz and absolutely continuous functions over irrational circle rotations, submitted for publication.
- [11] D. Volný, Constructions of smooth and analytic cocycles over irrational circle rotations, Comment. Math. Univ. Carolin. 36. (1995), 745-764. Zbl0866.28014

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