Ensemble d'invariants pour les produits croisés de Anzai
Mémoires de la Société Mathématique de France, no. 47 (1991) , 110 p. 
@book{MSMF_1991_2_47__1_0,
     author = {Gabriel, Pierre and Lemanczyk, M. and Liardet, Pierre},
     title = {Ensemble d'invariants pour les produits crois\'es de {Anzai}},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {47},
     year = {1991},
     doi = {10.24033/msmf.360},
     zbl = {0754.28011},
     mrnumber = {93b:28042},
     language = {fr},
     url = {http://archive.numdam.org/item/MSMF_1991_2_47__1_0/}
}
TY  - BOOK
AU  - Gabriel, Pierre
AU  - Lemanczyk, M.
AU  - Liardet, Pierre
TI  - Ensemble d'invariants pour les produits croisés de Anzai
T3  - Mémoires de la Société Mathématique de France
PY  - 1991
DA  - 1991///
IS  - 47
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/MSMF_1991_2_47__1_0/
UR  - https://zbmath.org/?q=an%3A0754.28011
UR  - https://www.ams.org/mathscinet-getitem?mr=93b:28042
UR  - https://doi.org/10.24033/msmf.360
DO  - 10.24033/msmf.360
LA  - fr
ID  - MSMF_1991_2_47__1_0
ER  - 
Gabriel, P.; Lemanczyk, M.; Liardet, P. Ensemble d'invariants pour les produits croisés de Anzai. Mémoires de la Société Mathématique de France, Série 2, , no. 47 (1991), 110 p. doi : 10.24033/msmf.360. http://numdam.org/item/MSMF_1991_2_47__1_0/

[Ab] Abramov (L.M.). - Metric automorphisms with quasi discrete spectrum, Ivs. Akad. Nauk. SSSR Ser. Math. 26, (1962), p. 513-530 [Amer. Math. Soc. Transl. (2) 39, (1964), p. 37-56]. | MR 26 #606 | Zbl 0154.15704

[An] Anzai (H.). - Ergodic skew product transformations on the torus, Osaka J. Math., 3, 1951, p. 83-99. | MR 12,719d | Zbl 0043.11203

[Ba 1] Baggett (L.). - On functions that are trivial cocycles for a set of irrationals, Proc. Amer. Math. Soc., 104, No 4, 1988, p. 1212-1215. | MR 89h:28022a | Zbl 0692.28008

[Ba 2] Baggett (L.). - On circle-valued cocycles of an ergodic measure-preserving transformation, Israel J. Math., 61, No 1, 1988, p. 29-38. | MR 89g:28021 | Zbl 0652.28004

[Con-Les] Conze (J-P.), Lesigne (E.). - Sur un théorème ergodique pour des mesures diagonales, C. R. Ac. Sc., Paris, 306, Série 1, 1988, p. 491-493. | MR 89e:22012 | Zbl 0641.28010

[Co-Si-Fo] Cornfeld (I.P.), Sinai (Ya. G.), Fomin (S.V.). - Ergodic Theory. - Springer-Verlag, Berlin - Gottingen - Heidelberg, 1982 (Die Grundlehren der mathematischen Wissenschaften, 245). | Zbl 0493.28007

[Fü] Furstenberg (H.). - Strict ergodicity and transformations on the torus, Amer. J. Math. 89, 1961, p. 573-601. | MR 24 #A3263 | Zbl 0178.38404

[Fü] Furstenberg (H.). - Recurrence in Ergodic Theory and Combinatorial Number Theory. - Princeton University Press, Princeton, New Jersey, 1981. | MR 82j:28010 | Zbl 0459.28023

[Ga-Le-Me] Gabriel (P.), Lemańczyk (M.), Mentzen (M.K.). - Two-point cocycles with strong ergodicity property, Bull. Pol. Ac. Sc., à paraître. | Zbl 0759.28011

[Go-He] Gottschalk (W.H.), Hedlund (G.A.). - Topological Dynamics. - Amer. Math. Soc. Colloq. Pub. Vol 36, 1955. | MR 17,650e | Zbl 0067.15204

[Ha-Pa] Hahn (H.), Parry (W.). - Some characteristic properties of dynamical systems with quasi-discrete spectrum, Math. Syst. Th. 2, 1968, p. 179-198. | Zbl 0167.32902

[He-La] Hellekalek (P.), Larcher (G.). - On Weyl sums and skew products over irrational rotations, Theor. Comp. Sc., Fundamental Studies, 65-2, 1989, p. 189-196. | MR 90m:28019 | Zbl 0674.28008

[Hel] Helson (H.). - Cocycles on the circle, J. Operator Theory, 16, 1986, p. 189-199. | MR 88f:22020 | Zbl 0644.43003

[Hew-Ro] Hewitt (E.), Ross (K.). - Astract Harmonic Analysis II, Springer-Verlag, Berlin - Gottingen - Heidelberg, 1970. (Die Grundlehren der mathematischen Wissenschaften, 152). | MR 41 #7378 | Zbl 0830.43001

[Hl] Hlawka (E.). - Discrepancy and Riemann integration, in L. Mirsky (Ed.), Studies in Pure Mathematics (Papers presented to Richard Rado), Acad. Press, New York, 1971, p. 121-129. | MR 43 #3407 | Zbl 0218.10064

[Ju-Ru] Del Junco (A.), Rudolph (D.). - On the ergodic actions whose self-joinings are graphs, Erg. Th. & Dyn. Syst., 7, No 4, 1987, p. 531-558. | MR 89e:28029 | Zbl 0646.60010

[Ju-Le] Del Junco (A.), Lemańczyk (M.). - Generic spectral properties of measure-preserving maps and applications, preprint.

[Ko] Kočergin (A.V.). - On the homology of function over dynamical system, Dokl. AN SSSR, 231, 1976, Soviet Math. Dokl. 17, 1976, No 6, p. 1637-1641. | Zbl 0414.28024

[Kra-Li] Kraaikamp (C.), Liardet (P.). - Good approximations and continued fractions, Proceedings Amer. Math. Soc., à paraître. | Zbl 0725.11033

[Kr] Kronecker (K.). - Berliner Sitzungsberichte, 11 Dec. 1884, Werke 3, 1884, p. 49.

[Ku-Ni] Kuipers (L.), Niederreiter (H.). - Uniform Distribution of Sequences, John Wiley & Sons, 1974. | MR 54 #7415 | Zbl 0281.10001

[Kw-Le-Ru] Kwiatkowski (J.), Lemańczyk (M.), Rudolph (D.). - Weak isomorphism of measure-preserving diffeomorphisms, preprint.

[La] Larcher (G.). - A convergence problem connected with continued fractions, Proceedings Amer. Math. Soc., 103, 1988, p. 718-722. | MR 89i:11077 | Zbl 0659.10009

[Le 1] Lemańczyk (M.). - Weakly isomorphic transformations that are not isomorphic, Probab. Th. Rel. Fields, 78, 1988, p. 491-507. | MR 89h:28028 | Zbl 0628.60015

[Le 2] Lemańczyk (M.). - On the weak isomorphism of strictly ergodic homeomorphisms, Monatsh. Math., 108, No 1, 1989, p. 39-46. | MR 90g:28022 | Zbl 0679.28008

[Le-Li] Lemańczyk (M.), Liardet (P.). - Coalescence of Anzai skew products, preprint.

[Le-Me] Lemańczyk (M.), Mentzen (M.K.). - Compact subgroups in the centralizers of the natural factors of an ergodic group extension of a rotation determine all factors, Erg. Th. & Dyn. Syst., 10, 1990, p 763-776. | MR 92g:22019 | Zbl 0725.54030

[Les] Lesigne (E.). - Résolution d'une équation fonctionnelle, Bull. Soc. Math. France, 112, 1984, p. 177-196. | Numdam | MR 86k:22018 | Zbl 0595.28019

[Me] Merill (K.). - Cohomology of step functions over irrational rotations, Israel J. Math., 52(4), 1985, p. 320-340. | Zbl 0616.28010

[Ne 1] Newton (D.). - Coalescence and spectrum of automorphisms of a Lebesgue space, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 19, 1971, p. 117-122. | MR 44 #6936 | Zbl 0201.38401

[Ne 2] Newton (D.). - On canonical factors of ergodic dynamical systems, J. London Math. Soc., 19, 1979, p. 129-136. | MR 80c:28012 | Zbl 0425.28012

[Os] Ostrowsi (A.). - Bemerkungen zur Theorie der diophantischen Approximationen, Abh. Math. Sem. Hamburg Univ. 1, (1922), p. 77-98. | JFM 48.0185.01

[Pa 1] Parry (W.). - A note on cocycles in ergodic theory, Compositio Math., 28, 1966, p. 303-330. | Numdam | MR 50 #4894 | Zbl 0287.28011

[Pa 2] Parry (W.). - Compact abelian group extensions of discrete dynamical systems, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 19, 1969, p. 95-113. | MR 41 #5596 | Zbl 0184.26901

[Pe] Perron (O.). - Die Lehre von den Kettenbrüchen. - 3. Aufl., B.G. Teubner, Stuttgart, 1954. | Zbl 0056.05901

[Ru 1] Rudolph (D.). - An example of a measure-preserving map with minimal self-joinings and applications, J. Analyse. Math., 35, 1979, p. 97-122. | MR 81e:28011 | Zbl 0446.28018

[Ru 2] Rudolph (D.). - Zn and Rn cocycle extensions and complementary algebras, Ergod. Th. & Dynam. Sys., 6, 1986, p. 583-599. | MR 88b:28032 | Zbl 0625.28008

[Sc] Schmidt (K.). - Cocycles of Ergodic Transformation Groups. - Macmillan Lectures Math., vol 1, Macmillan Compagny of India, 1977. | MR 58 #28262 | Zbl 0421.28017

[Si] Sinai (Ya. G.). - On weak isomorphism of transformations with invariant measure (in Russian), Math. Sb., 63, 1963, p. 23-42 [Amer. Math. Sco. Transl. (2) 52, 1966, p. 123-143].

[Th] Thouvenot (J.P.). - The metrical structure of some Gaussian processes, Proc. Erg. Th. Rel. Topics, II, Georgenthal 1986, p. 195-198. | MR 89m:28029 | Zbl 0653.28014

[Ve] Veech (W. A.). - Finite group extensions of irrational rotations, Israel J. Math., 21, 1975, p. 240-259. | MR 53 #773 | Zbl 0334.28014

Cité par Sources :