BV coboundaries over irrational rotations

Dalibor Volný

Studia Mathematica (1997)

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

Abstract

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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.

How to cite

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Volný, 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

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  1. [1] W. Bułatek, M. Lemańczyk and D. Rudolph, Constructions of cocycles over irrational rotations, Studia Math. 125 (1997), 1-11. Zbl0891.28011
  2. [2] H. Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math. 89 (1961), 573-601. Zbl0178.38404
  3. [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. [4] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95. Zbl0786.28011
  5. [5] A. Ya. Khintchine, Continued Fractions, Noordhoff, Groningen, 1963. 
  6. [6] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
  7. [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. [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. [9] K. Schmidt, Cocycles of Ergodic Transformation Groups, Macmillan Lectures in Math. 1, Macmillan of India, 1977. 
  10. [10] D. Volný, Cohomology of Lipschitz and absolutely continuous functions over irrational circle rotations, submitted for publication. 
  11. [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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