Most monothetic extensions are rank-1

• Autorzy: Anzelm Iwanik , Jacek Serafin
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1993
• Tom: 66
• Numer: 1
• Strony: 63-76

Daty

wydano

1993

otrzymano

1993-02-18

Twórcy

autor

Anzelm Iwanik

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

autor

Jacek Serafin

• Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Bibliografia

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• [B] L. Baggett, On functions that are trivial cocycles for a set of irrationals, Proc. Amer. Math. Soc. 104 (1988), 1212-1217.
• [Ba] J. R. Baxter, A class of ergodic transformations having simple spectrum, ibid. 27 (1971), 275-279.
• P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Suppl. Bull. Soc. Math. France 119 (3) (1991), Mém. 47.
• [J-P] R. Jones and W. Parry, Compact abelian group extensions of dynamical systems II, Compositio Math. 25 (1972), 135-147.
• [J] A. del Junco, Transformations with discrete spectrum are stacking transformations, Canad. J. Math. 28 (1976), 836-839.
• [K-S] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspekhi Mat. Nauk 22 (1967), 81-106 (in Russian); English transl.: Russian Math. Surveys 22 (1967), 77-102.
• [P] B. J. Pettis, On continuity and openness of homomorphisms in topological groups, Ann. of Math. 52 (1950), 293-308.
• [R1] E. A. Robinson, Ergodic measure preserving transformations with arbitrary finite spectral multiplicities, Invent. Math. 72 (1983), 299-314.
• [R2] E. A. Robinson, Non-abelian extensions have nonsimple spectrum, Compositio Math. 65 (1988), 155-170.
• [Ru] D. J. Rudolph, $ℤ^n$ and $ℝ^n$ cocycle extensions and complementary algebras, Ergodic Theory Dynamical Systems 6 (1986), 583-599.