no. 2
Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy-Rees technique
Béguin, François1 ; Crovisier, Sylvain ; Le Roux, Frédéric
1 École Normale Supérieure de Lyon, UMPA, 46 allée d'Italie, 69364 Lyon Cedex 07 (France)
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 2, pp. 251-308.
DOI : 10.1016/j.ansens.2007.01.001
Béguin, François 1 ; Crovisier, Sylvain  ; Le Roux, Frédéric 

1 École Normale Supérieure de Lyon, UMPA, 46 allée d'Italie, 69364 Lyon Cedex 07 (France) 
@article{ASENS_2007_4_40_2_251_0,
     author = {B\'eguin, Fran\c{c}ois and Crovisier, Sylvain and Le Roux, Fr\'ed\'eric},
     title = {Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the {Denjoy-Rees} technique},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {251--308},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {2},
     year = {2007},
     doi = {10.1016/j.ansens.2007.01.001},
     zbl = {1132.37003},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2007.01.001/}
}
TY  - JOUR
AU  - Béguin, François
AU  - Crovisier, Sylvain
AU  - Le Roux, Frédéric
TI  - Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy-Rees technique
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2007
SP  - 251
EP  - 308
VL  - 40
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.ansens.2007.01.001/
DO  - 10.1016/j.ansens.2007.01.001
LA  - en
ID  - ASENS_2007_4_40_2_251_0
ER  - 
%0 Journal Article
%A Béguin, François
%A Crovisier, Sylvain
%A Le Roux, Frédéric
%T Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy-Rees technique
%J Annales scientifiques de l'École Normale Supérieure
%D 2007
%P 251-308
%V 40
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.ansens.2007.01.001/
%R 10.1016/j.ansens.2007.01.001
%G en
%F ASENS_2007_4_40_2_251_0
Béguin, François; Crovisier, Sylvain; Le Roux, Frédéric. Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy-Rees technique. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 40 (2007) no. 2, pp. 251-308. doi : 10.1016/j.ansens.2007.01.001. http://www.numdam.org/articles/10.1016/j.ansens.2007.01.001/

[1] Anosov D., Katok A., New examples in smooth ergodic theory. Ergodic diffeomorphisms, Trans. Moscow Math. Soc. 23 (1970) 1-35. | MR | Zbl

[2] Béguin F., Crovisier S., Le Roux F., Patou A., Pseudo-rotations of the closed annulus: variation on a theorem of J. Kwapisz, Nonlinearity 17 (4) (2004) 1427-1453. | MR | Zbl

[3] Béguin F., Crovisier S., Le Roux F., Pseudo-rotations of the open annulus: variation on a theorem of J. Kwapisz, Bull. Braz. Math. Soc. (N.S.) 37 (2006) 275-306. | MR | Zbl

[4] Béguin F., Crovisier S., Jaeger T., Le Roux F., Denjoy constructions for fibered homeomorphism of the two-torus, in preparation.

[5] Bing R.H., Tame Cantor sets in E 3 , Pacific J. Math. 11 (1961) 435-446. | MR | Zbl

[6] Bing R.H., The Geometric Topology of 3-Manifolds, American Mathematical Society Colloquium Publications, vol. 40, American Mathematical Society, Providence, RI, 1983. | MR | Zbl

[7] Brown M., A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960) 74-76. | MR | Zbl

[8] Denjoy A., Sur les courbes définies par les équations différentielles à la surface du tore, J. Math. Pures Appl. Ser. IX 11 (1932) 333-375. | Numdam | Zbl

[9] Denker M., Grillenberger C., Sigmund K., Ergodic Theory on Compact Spaces, Springer Lecture Notes in Math., vol. 527, Springer-Verlag, Berlin/New York, 1976. | MR | Zbl

[10] Fathi A., Herman M., Existence de difféomorphismes minimaux, in: Dynamical Systems, vol. I, Warsaw, Astérisque, vol. 49, Soc. Math. France, Paris, 1977, 37-59. | Numdam | Zbl

[11] Fayad B., Katok A., Constructions in elliptic dynamics, Ergodic Theory Dynam. Systems 24 (5) (2004) 1477-1520. | MR | Zbl

[12] Handel M., A pathological area preserving C ∞ diffeomorphism of the plane, Proc. Amer. Math. Soc. 86 (1) (1982) 163-168. | MR | Zbl

[13] Herman M., Construction d'un difféomorphisme minimal d'entropie topologique non-nulle, Ergodic Theory Dynam. Systems 1 (1981) 65-76. | MR | Zbl

[14] Herman M., Construction of some curious diffeomorphisms of the Riemann sphere, J. London Math. Soc. (2) 34 (2) (1986) 375-384. | MR | Zbl

[15] Homma T., On tame imbedding of 0-dimensional compact sets in E 3 , Yokohama Math. J. 7 (1959) 191-195. | MR | Zbl

[16] Jäger T., Stark J., Towards a classification for quasi-periodically forced circle homeomorphisms, J. London Math. Soc. 73 (2006) 727-744. | MR | Zbl

[17] Katok A., Lyapounov exponents, entropy and periodic orbits for diffeomorphisms, Publications Mathématiques de l'I.H.É.S. 51 (1980) 131-173. | Numdam | MR | Zbl

[18] Le Calvez P., Rotation numbers in the infinite annulus, Proc. Amer. Math. Soc. 129 (11) (2001) 3221-3230. | MR | Zbl

[19] Lind D., Thouvenot J.-P., Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations, Math. Systems Theory 11 (3) (1977/78) 275-282. | MR | Zbl

[20] Osborne R.P., Embedding Cantor sets in a manifold. I. Tame Cantor sets in E n , Michigan Math. J. 13 (1966) 57-63. | MR | Zbl

[21] Oxtoby J.C., Ulam S.M., Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941) 874-920. | MR | Zbl

[22] Rees M., A minimal positive entropy homeomorphism of the 2-torus, J. London Math. Soc. 23 (1981) 537-550. | MR | Zbl

[23] Sanford M.D., Walker R.B., Extending maps of a Cantor set product with an arc to near homeomorphisms of the 2-disk, Pacific J. Math. 192 (2) (2000) 369-384. | MR | Zbl

[24] Thouvenot J.-P., Entropy, isomorphisms and equivalence, in: Katok A., Hasselblatt B. (Eds.), Handbook of Dynamical Systems, vol. 1A, Elsevier, Amsterdam, 2002. | MR | Zbl

Cité par Sources :