Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle

Jean-Marc Derrien

Bulletin de la Société Mathématique de France (1997)

  • Volume: 125, Issue: 2, page 227-248
  • ISSN: 0037-9484

How to cite

top

Derrien, Jean-Marc. "Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle." Bulletin de la Société Mathématique de France 125.2 (1997): 227-248. <http://eudml.org/doc/87763>.

@article{Derrien1997,
author = {Derrien, Jean-Marc},
journal = {Bulletin de la Société Mathématique de France},
keywords = {functional equations; step cocycles; irrational rotation; ergodic; weakly mixing},
language = {fre},
number = {2},
pages = {227-248},
publisher = {Société mathématique de France},
title = {Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle},
url = {http://eudml.org/doc/87763},
volume = {125},
year = {1997},
}

TY - JOUR
AU - Derrien, Jean-Marc
TI - Construction de cocycles en escalier ergodiques et faiblement mélangeants au-dessus de rotations irrationnelles du cercle
JO - Bulletin de la Société Mathématique de France
PY - 1997
PB - Société mathématique de France
VL - 125
IS - 2
SP - 227
EP - 248
LA - fre
KW - functional equations; step cocycles; irrational rotation; ergodic; weakly mixing
UR - http://eudml.org/doc/87763
ER -

References

top
  1. [1]ANZAÏ (H.). — Ergodic skew product transformations on the torus, Osaka J. Math., t. 3, 1951, p. 83-99. Zbl0043.11203MR12,719d
  2. [2]BURNSIDE (W.). — Theory of groups of finite order. — Dover Publications, 1911. 
  3. [3]CONZE (J.-P.). — Équirépartition et ergodicité de transformations cylindriques, Séminaire de Probabilité, Université de Rennes, 1976. MR58 #28425
  4. [4]DERRIEN (J.-M.). — Critères d'ergodicité de cocycles en escalier. Exemples, C. R. Acad. Sci. Paris, t. 316, Série I, 1993, p. 73-76. Zbl0771.58029MR93j:28030
  5. [5]FURSTENBERG (H.). — Strict ergodicity and transformations of the torus, Am. J. Math., t. 88, 1961, p. 573-601. Zbl0178.38404MR24 #A3263
  6. [6]FURSTENBERG (H.). — Ergodic behaviour of diagonal measures and a theorem of Szemeredi on arithmetic progressions, J. Analyse Math., t. 34, 1978, p. 204-256. Zbl0347.28016
  7. [7]GABRIEL (P.), LEMAǸCZYK (M.), LIARDET (P.). — Ensemble d'invariants pour les produits croisés de Anzaï, Mémoire de la SMF, t. 47, 1991. Zbl0754.28011
  8. [8]HEWITT (E.), ROSS (K.A.). — Abstract Harmonic Analysis II. — Springer-Verlag, 1970. 
  9. [9]KWIATKOWSKI (J.), LEMAǸCZYK (M.), RUDOLPH (D.). — Weak isomorphism of measure-preserving diffeomorphisms, Israel J. Math., t. 80, 1992, p. 33-64. Zbl0774.28008MR95g:28029
  10. [10]LESIGNE (E.). — Ergodic theorem along a return time sequence, Ergodic theory and related topics III, Proc. 3rd Int. Conf., Guestrow/Ger. (1990), Lecture Notes Math., t. 1514, 1992, p. 146-152. Zbl0763.28011
  11. [11]LESIGNE (E.), MAUDUIT (C.), MOSSE (B.). — Le théorème ergodique le long d'une suite q-multiplicative, Compositio Mathematica, t. 93, 1994, p. 49-79. Zbl0818.28006MR95h:11075
  12. [12]LIARDET (P.). — Répartion et ergodicité, Séminaire Delange-Pisot-Poitou (Théorie des nombres), 19e année, t. 10, (1977/1978). Zbl0392.10048
  13. [13]MACKEY (G.W.). — Induced representation of locally compact groups, 1, Ann. of Math., t. 55, 1952, p. 101-139. Zbl0046.11601MR13,434a
  14. [14]MERRILL (K.D.). — Cohomology of step functions under irrationnal rotations, Israel J. Math., t. 52, n° 4, 1985, p. 320-340. Zbl0616.28010MR88b:39009
  15. [15]VEECH (W.A.). — Strict ergodicity in zero dimensionnal dynamical systems and the Kronecker-Weyl theorem Mod 2, Trans. Am. Math. Soc., t. 140, 1969, p. 1-33. Zbl0201.05601MR39 #1410
  16. [16]VEECH (W.A.). — Finite group extensions of irrational rotations, Israel J. Math., t. 21, 1975, p. 240-259. Zbl0334.28014MR53 #773
  17. [17]ZIMMER (R.J.). — Ergodic actions with generalized discrete spectrum, Illinois J. Math., t. 20, 1976, p. 555-588. Zbl0349.28011MR54 #2924
  18. [18]ZIMMER (R.J.). — Extensions of ergodic group actions, Illinois J. Math., t. 20, 1976, p. 373-409. Zbl0334.28015MR53 #13522

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.