Spectral properties of skew-product diffeomorphisms of tori

A. Iwanik

Colloquium Mathematicum (1997)

  • Volume: 72, Issue: 2, page 223-235
  • ISSN: 0010-1354

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Iwanik, A.. "Spectral properties of skew-product diffeomorphisms of tori." Colloquium Mathematicum 72.2 (1997): 223-235. <http://eudml.org/doc/210461>.

@article{Iwanik1997,
author = {Iwanik, A.},
journal = {Colloquium Mathematicum},
keywords = {countable Lebesgue spectrum; Anzai skew-products; weakly mixing cocycles},
language = {eng},
number = {2},
pages = {223-235},
title = {Spectral properties of skew-product diffeomorphisms of tori},
url = {http://eudml.org/doc/210461},
volume = {72},
year = {1997},
}

TY - JOUR
AU - Iwanik, A.
TI - Spectral properties of skew-product diffeomorphisms of tori
JO - Colloquium Mathematicum
PY - 1997
VL - 72
IS - 2
SP - 223
EP - 235
LA - eng
KW - countable Lebesgue spectrum; Anzai skew-products; weakly mixing cocycles
UR - http://eudml.org/doc/210461
ER -

References

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  1. [A] H. Anzai, Ergodic skew product transformations on the torus, Osaka Math. J. 3 (1951), 83-99. 
  2. [B] L. Baggett, On functions that are trivial cocycles for a set of irrationals, Proc. Amer. Math. Soc. 104 (1988), 1212-1217. 
  3. [C] G. H. Choe, Spectral properties of cocycles, Ph.D. Thesis, University of California, Berkeley, 1987. 
  4. [CFS] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, 1982. 
  5. [F] K. Frączek, Spectral properties of cocycles over rotations, preprint. 
  6. [I1] A. Iwanik, Approximation by periodic transformations and diophantine approximation of the spectrum, in: Ergodic Theory of Z d -Actions, Proc. Warwick Symposium 1993-4, Cambridge Univ. Press, 1996, 387-401. 
  7. [I2] A. Iwanik, Generic smooth cocycles of degree zero over irrational rotations, Studia Math. 115 (1995), 241-250. 
  8. [I3] A. Iwanik, Cyclic approximation of analytic cocycles over irrational rotations, Colloq. Math. 70 (1996), 73-78. 
  9. [I4] A. Iwanik, Anzai skew products with Lebesgue component of infinite multiplicity, Bull. London Math. Soc., to appear. 
  10. [ILR] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95. 
  11. [IS] A. Iwanik and J. Serafin, Most monothetic extensions are rank-1, Colloq. Math. 66 (1993), 63-76. 
  12. [JP] R. Jones and W. Parry, Compact abelian group extensions of dynamical systems II, Compositio Math. 25 (1972), 135-147. 
  13. [KS] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspekhi Mat. Nauk 22 (5) (1967), 81-106 (in Russian). 
  14. [K] A. G. Kushnirenko, Spectral properties of some dynamical systems with polynomial divergence of orbits, Vestnik Moskov. Univ. 1974 (1), 101-108 (in Russian). 
  15. [R] A. Robinson, Non-abelian extensions have nonsimple spectrum, Compositio Math. 65 (1988), 155-170. 
  16. [Z] Q. Zhang, Rigidity of smooth cocycles over irrational rotations, preprint. 

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