On manifolds supporting quasi-Anosov diffeomorphisms
Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 321-323.

Let M be an n-dimensional manifold supporting a quasi-Anosov diffeomorphism. If n=3 then either M=𝕋 3 , in which case the diffeomorphisms is Anosov, or else its fundamental group contains a copy of 6 . If n=4 then Π1(M) contains a copy of 4 , provided that the diffeomorphism is not Anosov.

Soit M une variété différentiable de dimension n qui admet un difféomorphisme de type quasi-Anosov. Si n=3 alors on a l'altenative suivante, ou bien M=𝕋 3 , et dans ce cas le difféomorphisme est en fait d'Anosov, ou bien le goupe fondamental de M contient une copie de 6 . Si n=4, alors Π1(M) contient une copie de 4 , pourvu que le difféomorphisme ne soit pas d'Anosov.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02260-4
Rodriguez Hertz, Jana 1; Ures, Raúl 1; Vieitez, José L. 1

1 CC 30, IMERL – Facultad de Ingenierı́a, Universidad de la República, Montevideo, Uruguay
@article{CRMATH_2002__334_4_321_0,
     author = {Rodriguez Hertz, Jana and Ures, Ra\'ul and Vieitez, Jos\'e L.},
     title = {On manifolds supporting {quasi-Anosov} diffeomorphisms},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {321--323},
     publisher = {Elsevier},
     volume = {334},
     number = {4},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02260-4},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02260-4/}
}
TY  - JOUR
AU  - Rodriguez Hertz, Jana
AU  - Ures, Raúl
AU  - Vieitez, José L.
TI  - On manifolds supporting quasi-Anosov diffeomorphisms
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 321
EP  - 323
VL  - 334
IS  - 4
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02260-4/
DO  - 10.1016/S1631-073X(02)02260-4
LA  - en
ID  - CRMATH_2002__334_4_321_0
ER  - 
%0 Journal Article
%A Rodriguez Hertz, Jana
%A Ures, Raúl
%A Vieitez, José L.
%T On manifolds supporting quasi-Anosov diffeomorphisms
%J Comptes Rendus. Mathématique
%D 2002
%P 321-323
%V 334
%N 4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02260-4/
%R 10.1016/S1631-073X(02)02260-4
%G en
%F CRMATH_2002__334_4_321_0
Rodriguez Hertz, Jana; Ures, Raúl; Vieitez, José L. On manifolds supporting quasi-Anosov diffeomorphisms. Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 321-323. doi : 10.1016/S1631-073X(02)02260-4. http://www.numdam.org/articles/10.1016/S1631-073X(02)02260-4/

[1] Franks, J.; Robinson, C. A quasi-Anosov diffeomorphism that is not Anosov, Trans. Amer. Math. Soc., Volume 223 (1976), pp. 267-278

[2] Hiraide, K. Expansive homeomorphisms of surfaces are pseudo-Anosov, Osaka J. Math., Volume 27 (1990), pp. 117-162

[3] Hiraide, K. Dynamical systems of expansive maps on compact manifolds, Sugaku Expo., Volume 5 (1992), pp. 133-154

[4] Lewowicz, J. Expansive homeomorphisms of surfaces, Bol. Soc. Brasil. Mat., Volume 20 (1989) no. 1, pp. 113-133

[5] Mañé, R. Quasi-Anosov diffeomorphisms and hyperbolic manifolds, Trans. Amer. Math. Soc., Volume 229 (1977), pp. 351-370

[6] Mañé, R. Expansive diffeomorphisms, Lecture Notes in Math., 468, Springer-Verlag, 1975, pp. 162-174

[7] R. Mañé, Personal communication

[8] Plykin, R. Hyperbolic attractors of diffeomorphisms, Russian Math. Surveys, Volume 35 (1980) no. 3, pp. 109-121

[9] Plykin, R. On hyperbolic attractors of diffeomorphisms (the non-orientable case), Russian Math. Surveys, Volume 35 (1980) no. 4, pp. 186-187

[10] Smale, S. Differentiable dynamical systems, Bull. Amer. Math. Soc., Volume 73 (1967), pp. 747-817

[11] J. Vieitez, Lyapunov functions and expansive diffeomorphisms on 3D-manifolds, Ergodic Theory Dynam. Systems (to appear)

Cited by Sources:

The first author was partially supported by a grant from PEDECIBA. The second author was partially supported by CONICYT, Fondo Clemente Estable.