Construction of curious minimal uniquely ergodic homeomorphisms on manifolds : the Denjoy-Rees technique
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 40 (2007) no. 2, p. 251-308
@article{ASENS_2007_4_40_2_251_0,
     author = {B\'eguin, Fran\c cois 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},
     publisher = {Elsevier},
     volume = {Ser. 4, 40},
     number = {2},
     year = {2007},
     pages = {251-308},
     doi = {10.1016/j.ansens.2007.01.001},
     zbl = {1132.37003},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 4, Volume 40 (2007) no. 2, pp. 251-308. doi : 10.1016/j.ansens.2007.01.001. http://www.numdam.org/item/ASENS_2007_4_40_2_251_0/

[1] Anosov D., Katok A., New examples in smooth ergodic theory. Ergodic diffeomorphisms, Trans. Moscow Math. Soc. 23 (1970) 1-35. | MR 370662 | Zbl 0255.58007

[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 2069713 | Zbl 1077.37032

[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 2266384 | Zbl 1105.37029

[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 130679 | Zbl 0111.18606

[6] Bing R.H., The Geometric Topology of 3-Manifolds, American Mathematical Society Colloquium Publications, vol. 40, American Mathematical Society, Providence, RI, 1983. | MR 728227 | Zbl 0535.57001

[7] Brown M., A proof of the generalized Schoenflies theorem, Bull. Amer. Math. Soc. 66 (1960) 74-76. | MR 117695 | Zbl 0132.20002

[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. | Zbl 0006.30501

[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 457675 | Zbl 0328.28008

[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. | Zbl 0374.58010

[11] Fayad B., Katok A., Constructions in elliptic dynamics, Ergodic Theory Dynam. Systems 24 (5) (2004) 1477-1520. | MR 2104594 | Zbl 1089.37012

[12] Handel M., A pathological area preserving C diffeomorphism of the plane, Proc. Amer. Math. Soc. 86 (1) (1982) 163-168. | MR 663889 | Zbl 0509.58031

[13] Herman M., Construction d'un difféomorphisme minimal d'entropie topologique non-nulle, Ergodic Theory Dynam. Systems 1 (1981) 65-76. | MR 627787 | Zbl 0469.58008

[14] Herman M., Construction of some curious diffeomorphisms of the Riemann sphere, J. London Math. Soc. (2) 34 (2) (1986) 375-384. | MR 856520 | Zbl 0603.58017

[15] Homma T., On tame imbedding of 0-dimensional compact sets in E 3 , Yokohama Math. J. 7 (1959) 191-195. | MR 124037 | Zbl 0094.36005

[16] Jäger T., Stark J., Towards a classification for quasi-periodically forced circle homeomorphisms, J. London Math. Soc. 73 (2006) 727-744. | MR 2241977 | Zbl 1095.37013

[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 573822 | Zbl 0445.58015

[18] Le Calvez P., Rotation numbers in the infinite annulus, Proc. Amer. Math. Soc. 129 (11) (2001) 3221-3230. | MR 1844997 | Zbl 0990.37029

[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 584588 | Zbl 0377.28011

[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 187225 | Zbl 0138.18902

[21] Oxtoby J.C., Ulam S.M., Measure-preserving homeomorphisms and metrical transitivity, Ann. of Math. (2) 42 (1941) 874-920. | MR 5803 | Zbl 0063.06074

[22] Rees M., A minimal positive entropy homeomorphism of the 2-torus, J. London Math. Soc. 23 (1981) 537-550. | MR 616561 | Zbl 0451.58022

[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 1744576 | Zbl 1092.37502

[24] Thouvenot J.-P., Entropy, isomorphisms and equivalence, in: Katok A., Hasselblatt B. (Eds.), Handbook of Dynamical Systems, vol. 1A, Elsevier, Amsterdam, 2002. | MR 1928517 | Zbl 1084.37007