A class of nonstationary adic transformations

Xavier Méla

Annales de l'I.H.P. Probabilités et statistiques (2006)

  • Volume: 42, Issue: 1, page 103-123
  • ISSN: 0246-0203

How to cite

top

Méla, Xavier. "A class of nonstationary adic transformations." Annales de l'I.H.P. Probabilités et statistiques 42.1 (2006): 103-123. <http://eudml.org/doc/77883>.

@article{Méla2006,
author = {Méla, Xavier},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Adic transformations; Ergodicity; Weak mixing; Loosely Bernoulli; Complexity; Binomial coefficients},
language = {eng},
number = {1},
pages = {103-123},
publisher = {Elsevier},
title = {A class of nonstationary adic transformations},
url = {http://eudml.org/doc/77883},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Méla, Xavier
TI - A class of nonstationary adic transformations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 1
SP - 103
EP - 123
LA - eng
KW - Adic transformations; Ergodicity; Weak mixing; Loosely Bernoulli; Complexity; Binomial coefficients
UR - http://eudml.org/doc/77883
ER -

References

top
  1. [1] R. Bollinger, C. Burchard, Lucas's theorem and some related results for extended Pascal triangles, Amer. Math. Monthly97 (3) (1990) 198-204. Zbl0741.11014MR1048430
  2. [2] B.A. Bondarenko, Generalized Pascal Triangles and Pyramids, their Fractals, Graphs and Applications, Fan, Tashkent, 1990. Zbl0706.05002MR1069753
  3. [3] T. de la Rue, E. Janvresse, The Pascal adic transformation is loosely Bernoulli, Ann. Inst. H. Poincaré Probab. Statist.40 (2004) 133-139. Zbl1044.28012MR2044811
  4. [4] J. Feldman, New K-automorphisms and a problem of Kakutani, Israel J. Math.24 (1976) 16-38. Zbl0336.28003MR409763
  5. [5] S. Ferenczi, Systèmes localement de rang un, Ann. Inst. H. Poincaré20 (1984) 35-51. Zbl0535.28010MR740249
  6. [6] N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics, and Combinatorics, Lecture Notes in Math., vol. 1794, Springer-Verlag, 2002. Zbl1014.11015MR1970385
  7. [7] A. Hajian, Y. Ito, S. Kakutani, Invariant measures and orbits of dissipative transformations, Adv. in Math9 (1972) 52-65. Zbl0236.28010MR302860
  8. [8] B. Host, Substitution subshifts and Bratteli diagrams, in: Blanchard F., Maass A., Nogueira A. (Eds.), Topics in Symbolic Dynamics and Applications, London Math. Soc. Lecture Note Ser., Cambridge University Press, 1999. Zbl0985.37012MR1776755
  9. [9] A. Katok, Time change, monotone equivalence, and standard dynamical systems, Dokl. Akad. Nauk SSSR223 (4) (1975) 789-792, (in Russian). Zbl0326.28025MR412383
  10. [10] A. Katok, Monotone equivalence in ergodic theory, Izv. Akad. Nauk SSSR Ser. Mat.41 (1) (1977) 104-157, (in Russian). Zbl0372.28020MR442195
  11. [11] A. Katok, E. Sataev, Standardness of rearrangement automorphisms of segments and flows on surfaces, Mat. Zametki20 (4) (1976) 479-488, (in Russian). Zbl0368.58010MR430210
  12. [12] H. Keynes, J. Robertson, Eigenvalue theorems in topological transformation groups, Trans. Amer. Math. Soc.139 (1969) 359-369. Zbl0176.20602MR237748
  13. [13] A. Livshitz, A sufficient condition for weak mixing of substitutions and stationary adic transformations, Math. Notes44 (1988) 920-925. Zbl0713.28011
  14. [14] E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math.1 (1878) 184-240. MR1505161JFM10.0134.05
  15. [15] X. Méla, Dynamical properties of the Pascal adic and related systems, Ph.D. thesis, University of North Carolina at Chapel Hill, 2002. 
  16. [16] X. Méla, K. Petersen, Dynamical properties of the Pascal adic transformation, Ergodic Theory Dynam. Systems25 (2005) 227-256. Zbl1069.37007MR2122921
  17. [17] D. Ornstein, D. Rudolph, B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc.37 (1982). Zbl0504.28019MR653094
  18. [18] W. Parry, Topics in Ergodic Theory, Cambridge University Press, 1981. Zbl0449.28016MR614142
  19. [19] K. Petersen, Ergodic Theory, Cambridge University Press, 1989. Zbl0676.28008MR1073173
  20. [20] K. Petersen, T. Adams, Binomial coefficient multiples of irrationals, Monatsh. Math.125 (4) (1998) 269-278. Zbl0956.28014MR1621682
  21. [21] K. Petersen, K. Schmidt, Symmetric Gibbs measures, Trans. Amer. Math. Soc.349 (7) (1997) 2775-2811. Zbl0873.28008MR1422906
  22. [22] B. Solomyak, On the spectral theory of adic transformations, Adv. Soviet Math.9 (1992) 217-230. Zbl0770.28012MR1166205
  23. [23] A. Vershik, Uniform algebraic approximation of shift and multiplicative operators, Dokl. Akad. Nauk SSSR218 (24) (1981) 526-529. Zbl0484.47005MR625756

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.