Analytic nonregular cocycles over irrational rotations

Mariusz Lemańczyk

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 4, page 727-735
  • ISSN: 0010-2628

Abstract

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Analytic cocycles of type I I I 0 over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.

How to cite

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Lemańczyk, Mariusz. "Analytic nonregular cocycles over irrational rotations." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 727-735. <http://eudml.org/doc/247755>.

@article{Lemańczyk1995,
abstract = {Analytic cocycles of type $III_0$ over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.},
author = {Lemańczyk, Mariusz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cocycle; special flow; weak mixing; cylinder flow; essential values; type analytic cocycle; coboundary; unbounded gaps; ergodic measure preserving transformation},
language = {eng},
number = {4},
pages = {727-735},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Analytic nonregular cocycles over irrational rotations},
url = {http://eudml.org/doc/247755},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Lemańczyk, Mariusz
TI - Analytic nonregular cocycles over irrational rotations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 4
SP - 727
EP - 735
AB - Analytic cocycles of type $III_0$ over an irrational rotation are constructed and an example of that type is given, where all corresponding special flows are weakly mixing.
LA - eng
KW - cocycle; special flow; weak mixing; cylinder flow; essential values; type analytic cocycle; coboundary; unbounded gaps; ergodic measure preserving transformation
UR - http://eudml.org/doc/247755
ER -

References

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  1. Aaronson J., Hamachi T., Schmidt K., Associated actions and uniqueness of cocycles, to appear in Proc. of Okayama Conference, 1992. Zbl1008.37003MR1402476
  2. Aaronson J., Lemańczyk M., Volný D., A salad of cocycles, preprint. 
  3. Golodets V.Ya., Sinel'shchikov S.D., Classification and structure of cocycles of amenable ergodic equivalence relations, preprint. Zbl0821.28010MR1272135
  4. Katok A.B., Constructions in Ergodic Theory, unpublished lecture notes. Zbl1130.37304
  5. Kočergin A.W., On the homology of functions over dynamical systems, Dokl. AN SSSR 281 (1976). (1976) MR0430211
  6. Kwiatkowski J., Lemańczyk M., Rudolph D., On the weak isomorphism of measure-preserving diffeomorphisms, Isr. J. Math. 80 (1992), 33-64. (1992) MR1248926
  7. Kwiatkowski J., Lemańczyk M., Rudolph D., A class of cocycles having an analytic coboundary modification, Isr. J. Math. 87 (1994), 337-360. (1994) MR1286834
  8. Moore C.C., Schmidt K., Coboundaries and homomorphisms for non-singular actions and a problem of H. Helson, Proc. London Math. Soc. (3) 40 (1980), 443-475. (1980) Zbl0428.28014MR0572015
  9. Schmidt K., Cocycles of Ergodic Transformation Groups, Lect. Notes in Math. Vol. 1, Mac Millan Co. of India, 1977. MR0578731
  10. Volný D., Constructions of smooth and analytic cocycles over irrational circle rotations, Comment. Math. Univ. Carolinae 36.4 (1995), 745-764. (1995) MR1378696

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