A class of nonstationary adic transformations
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 1, p. 103-123
@article{AIHPB_2006__42_1_103_0,
     author = {M\'ela, Xavier},
     title = {A class of nonstationary adic transformations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Elsevier},
     volume = {42},
     number = {1},
     year = {2006},
     pages = {103-123},
     doi = {10.1016/j.anihpb.2005.02.002},
     zbl = {05021195},
     mrnumber = {2196974},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2006__42_1_103_0}
}
Méla, Xavier. A class of nonstationary adic transformations. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 1, pp. 103-123. doi : 10.1016/j.anihpb.2005.02.002. http://www.numdam.org/item/AIHPB_2006__42_1_103_0/

[1] R. Bollinger, C. Burchard, Lucas's theorem and some related results for extended Pascal triangles, Amer. Math. Monthly 97 (3) (1990) 198-204. | MR 1048430 | Zbl 0741.11014

[2] B.A. Bondarenko, Generalized Pascal Triangles and Pyramids, their Fractals, Graphs and Applications, Fan, Tashkent, 1990. | MR 1069753 | Zbl 0706.05002

[3] T. De La Rue, E. Janvresse, The Pascal adic transformation is loosely Bernoulli, Ann. Inst. H. Poincaré Probab. Statist. 40 (2004) 133-139. | Numdam | MR 2044811 | Zbl 1044.28012

[4] J. Feldman, New K-automorphisms and a problem of Kakutani, Israel J. Math. 24 (1976) 16-38. | MR 409763 | Zbl 0336.28003

[5] S. Ferenczi, Systèmes localement de rang un, Ann. Inst. H. Poincaré 20 (1984) 35-51. | Numdam | MR 740249 | Zbl 0535.28010

[6] N. Pytheas Fogg, Substitutions in Dynamics, Arithmetics, and Combinatorics, Lecture Notes in Math., vol. 1794, Springer-Verlag, 2002. | MR 1970385 | Zbl 1014.11015

[7] A. Hajian, Y. Ito, S. Kakutani, Invariant measures and orbits of dissipative transformations, Adv. in Math 9 (1972) 52-65. | MR 302860 | Zbl 0236.28010

[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. | MR 1776755 | Zbl 0985.37012

[9] A. Katok, Time change, monotone equivalence, and standard dynamical systems, Dokl. Akad. Nauk SSSR 223 (4) (1975) 789-792, (in Russian). | MR 412383 | Zbl 0326.28025

[10] A. Katok, Monotone equivalence in ergodic theory, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1) (1977) 104-157, (in Russian). | MR 442195 | Zbl 0372.28020

[11] A. Katok, E. Sataev, Standardness of rearrangement automorphisms of segments and flows on surfaces, Mat. Zametki 20 (4) (1976) 479-488, (in Russian). | MR 430210 | Zbl 0368.58010

[12] H. Keynes, J. Robertson, Eigenvalue theorems in topological transformation groups, Trans. Amer. Math. Soc. 139 (1969) 359-369. | MR 237748 | Zbl 0176.20602

[13] A. Livshitz, A sufficient condition for weak mixing of substitutions and stationary adic transformations, Math. Notes 44 (1988) 920-925. | Zbl 0713.28011

[14] E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math. 1 (1878) 184-240. | JFM 10.0134.05 | MR 1505161

[15] X. Méla, Dynamical properties of the Pascal adic and related systems, Ph.D. thesis, University of North Carolina at Chapel Hill, 2002.

[16] X. Méla, K. Petersen, Dynamical properties of the Pascal adic transformation, Ergodic Theory Dynam. Systems 25 (2005) 227-256. | MR 2122921 | Zbl 1069.37007

[17] D. Ornstein, D. Rudolph, B. Weiss, Equivalence of measure preserving transformations, Mem. Amer. Math. Soc. 37 (1982). | MR 653094 | Zbl 0504.28019

[18] W. Parry, Topics in Ergodic Theory, Cambridge University Press, 1981. | MR 614142 | Zbl 0449.28016

[19] K. Petersen, Ergodic Theory, Cambridge University Press, 1989. | MR 1073173 | Zbl 0676.28008

[20] K. Petersen, T. Adams, Binomial coefficient multiples of irrationals, Monatsh. Math. 125 (4) (1998) 269-278. | MR 1621682 | Zbl 0956.28014

[21] K. Petersen, K. Schmidt, Symmetric Gibbs measures, Trans. Amer. Math. Soc. 349 (7) (1997) 2775-2811. | MR 1422906 | Zbl 0873.28008

[22] B. Solomyak, On the spectral theory of adic transformations, Adv. Soviet Math. 9 (1992) 217-230. | MR 1166205 | Zbl 0770.28012

[23] A. Vershik, Uniform algebraic approximation of shift and multiplicative operators, Dokl. Akad. Nauk SSSR 218 (24) (1981) 526-529. | MR 625756 | Zbl 0484.47005