Spectral properties of skew-product diffeomorphisms of tori

• Autorzy: Anzelm Iwanik
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 72
• Numer: 2
• Strony: 223-235

Daty

wydano

1997

otrzymano

1995-12-20

Twórcy

autor

Anzelm Iwanik

• Institute of Mathematics, Technical University of Wrocław, 50-370 Wrocław, Poland

Bibliografia

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