Geodesic
A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum
Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 316-322

Voir la notice de l'article provenant de la source Cambridge University Press

R. Ji asked whether or not a Furstenberg transformation of the 2-torus of the form (x,y) → (e2πiθx, f(x)y), where θ is irrational and f : T —> T is continuous with non-zero degree k, is topologically conjugate to the Anzai transformation (x, y) → (e2πiθx, xk y) or its inverse. In this paper this question is settled in the negative. Further, some sufficient conditions are given under which the crossed product C*-algebra associated with a Furstenberg transformation of the 2-torus has a unique tracial state.
DOI : 10.4153/CMB-1990-052-7
Mots-clés : 46L80 
Rouhani, H. A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum. Canadian mathematical bulletin, Tome 33 (1990) no. 3, pp. 316-322. doi: 10.4153/CMB-1990-052-7
@article{10_4153_CMB_1990_052_7,
     author = {Rouhani, H.},
     title = {A {Furstenberg} {Transformation} of the {2-Torus} {Without} {Quasi-Discrete} {Spectrum}},
     journal = {Canadian mathematical bulletin},
     pages = {316--322},
     year = {1990},
     volume = {33},
     number = {3},
     doi = {10.4153/CMB-1990-052-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-052-7/}
}
TY  - JOUR
AU  - Rouhani, H.
TI  - A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum
JO  - Canadian mathematical bulletin
PY  - 1990
SP  - 316
EP  - 322
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-052-7/
DO  - 10.4153/CMB-1990-052-7
ID  - 10_4153_CMB_1990_052_7
ER  - 
%0 Journal Article
%A Rouhani, H.
%T A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum
%J Canadian mathematical bulletin
%D 1990
%P 316-322
%V 33
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-052-7/
%R 10.4153/CMB-1990-052-7
%F 10_4153_CMB_1990_052_7

[1] 1. Baggett, L., and Merrill, K., Equivalence of cocycles under an irrational rotation, preprint. Google Scholar

[2] 2. Effros, E. G., and Hahn, F., Locally compact transformation groups and C*-aglebras, Memoirs of A.M.S., No. 75 (1967). Google Scholar

[3] 3. Furstenberg, H., Strict ergodicity and transformation of the torus, Amer. J. Math 83 (1961), No. 4, 573–601. Google Scholar

[4] 4. Gottschalk, W. H., and Hedlund, G. A., Topological Dynamics, Amer. Math. Soc. Coll. Publ., Vol. 36 (1955). Google Scholar

[5] 5. Ji, R., On the crossed product C* -algebras associated with Furstenberg transformations on tori, Ph.D. thesis, State University of New York at Stony Brook, 1986. Google Scholar

[6] 6. Parry, W., Topics in Ergodic Theory, (Cambridge Univ. Press, 1981). Google Scholar

[7] 7. Power, S. C., Simplicity of C*-algebras of minimal dynamical systems, J. London Math. Soc. 18 (1978), 534–8. Google Scholar

[8] 8. Rouhani, H., Classification of certain non-commutative three-tori, Ph.D. thesis, Dalhousie University, Halifax, N.S., Canada, 1988. Google Scholar

Cité par Sources :