Piecewise absolutely continuous cocycles over irrational rotations

Journal of the London Mathematical Society

Volumn 59, Issue 1, 1999, Pages 171-187

  Iwanik, A ^a   Lemanczyk M ^c   Mauduit, C ^b  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b AIX MARSEILLE UNIVERSITÉ   (France)

^c NICOLAUS COPERNICUS UNIVERSITY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0007466879     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0024610799006961     Document Type: Article

References (20)

1. J. AARONSON, M. LEMAŃCZYK, C. MAUDUIT and H. NAKADA, 'Koksma's inequality and group extensions of Kronecker transformations', Algorithms, fractals and dynamics (ed. Y. Takahashi; Plenum Press, 1995) 27-50.
2. H. ANZAI, 'Ergodic skew product transformations on the torus', Osaka J. Math. 3 (1951) 88-99.
3. G. H. CHOE, 'Products of operators with singular continuous spectra', Proc. Sympos. Pure Math. 51 (1990) 65-68.
4. I. P. CORNFELD, S. W. FOMIN and Y. G. SINAI, Ergodic theory (Springer, 1982).
5. J. DEPAUW, 'Théorèmes ergodiques pour cocycle de degré 2', Thèse de Doctorat, Université de Bretagne Occidentale, Brest, 1994.
6. J. FELDMAN and C. MOORE, 'Ergodic equivalence relations, cohomology, and von Neumann algebras, I', Trans. Amer. Math. Soc. 235 (1977) 289-324.
7. G. R. GOODSON, J. KWIATKOWSKI, M. LEMAŃCZYK and P. LIARDET, 'On the multiplicity function of ergodic group extensions of rotations', Studia Math. 102 (1992) 154-174.
8. M. GUENAIS, 'Une majoration de la multiplicité spectrale d'opérateurs associés à des cocycles réguliers', Israel J. Math. 105 (1998) 263-283.
9. G. H. HARDY and E. M. WRIGHT, An introduction to the theory of numbers (Oxford, 1954).
10. H. HELSON, 'Cocycles on the circle', J. Operator Theory 16 (1986) 189-199.
11. M. HERMAN, 'Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations', Publ. IHES 49 (1979) 5-234.
12. A. IWANIK, 'Anzai skew products with Lebesgue component of infinite multiplicity', Bull. London Math. Soc. (to appear).
13. A. IWANIK, M. LEMAŃCZYK and D. RUDOLPH, 'Absolutely continuous cocyles over irrational rotations', Israel J. Math. 83 (1993) 73-95.
14. A. KATOK, 'Constructions in ergodic theory', unpublished lecture notes.
15. M. LEMAŃCZYK and C. MAUDUIT, 'Ergodicity of a class of cocycles over irrational rotations', J. London Math. Soc. 49 (1994) 124-132.
16. H. A. MEDINA, 'Spectral types of unitary operators arising from irrational rotations on the circle group', Michigan Math. J. 41 (1994) 39-49.
17. D. A. PASK, 'Skew products over the irrational rotation', Israel J. Math. 69 (1990) 65-74.
18. D. A. PASK, 'Ergodicity of certain cylinder flows', Israel J. Math. 76 (1991) 129-152.
19. M. QUEFFÉLEC, Substitution dynamical systems - spectral analysis, Lecture Notes in Mathematics 1294 (Springer, Berlin, 1988).
20. M. WALDSCHMIDT, Nombres transcendants, Lecture Notes in Mathematics 402 (Springer, Berlin, 1974).