Polycyclic groups of diffeomorphisms of the closed interval

Yoshifumi Matsuda

doi:10.1016/j.crma.2009.04.008

Dynamical Systems

Polycyclic groups of diffeomorphisms of the closed interval

Presented by: Étienne Ghys

Yoshifumi Matsuda ¹

¹ Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan

Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 813-816.

Abstract
Résumé

We give a classification of polycyclic groups of orientation-preserving $C^{2}$ -diffeomorphisms of the closed interval. This shows that many polycyclic groups of $C^{2}$ -diffeomorphisms of the half-open interval are not the restriction of groups of $C^{2}$ -diffeomorphisms of the closed interval.

On donne une classification des groupes polycycliques de difféomorphismes directs et de classe $C^{2}$ de l'intervalle fermé. Cela montre que il y a des groupes polycycliques de difféomorphsmes de classe $C^{2}$ de l'intervalle demi-ouvert qui ne sont pas des restrictions des groupes de difféomorphsmes de classe $C^{2}$ de l'intervalle fermée.

Received: 2009-01-11
Accepted: 2009-04-07
Published online: 2009-05-06

DOI: 10.1016/j.crma.2009.04.008

Author's affiliations:

Yoshifumi Matsuda ¹

¹ Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro, Tokyo 153-8914, Japan

@article{CRMATH_2009__347_13-14_813_0,
     author = {Yoshifumi Matsuda},
     title = {Polycyclic groups of diffeomorphisms of the closed interval},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {813--816},
     publisher = {Elsevier},
     volume = {347},
     number = {13-14},
     year = {2009},
     doi = {10.1016/j.crma.2009.04.008},
     language = {en},
}

TY  - JOUR
AU  - Yoshifumi Matsuda
TI  - Polycyclic groups of diffeomorphisms of the closed interval
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 813
EP  - 816
VL  - 347
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2009.04.008
LA  - en
ID  - CRMATH_2009__347_13-14_813_0
ER  -

%0 Journal Article
%A Yoshifumi Matsuda
%T Polycyclic groups of diffeomorphisms of the closed interval
%J Comptes Rendus. Mathématique
%D 2009
%P 813-816
%V 347
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2009.04.008
%G en
%F CRMATH_2009__347_13-14_813_0

Yoshifumi Matsuda. Polycyclic groups of diffeomorphisms of the closed interval. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 813-816. doi : 10.1016/j.crma.2009.04.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.008/

References
Cited by

[1] S. Druck; S. Firmo Periodic leaves for diffeomorphisms preserving codimension one foliations, J. Math. Soc. Japan, Volume 55 (2003) no. 1, pp. 13-37

[2] C. Godbillon Feuielletages. Études géometriques, Progress in Mathematics, vol. 98, Birkhäuser, 1991

[3] N. Kopell Commuting diffeomorphisms, Berkeley, CA, 1968 (Proc. Sympos. Pure Math.), Volume vol. 14, Amer. Math. Soc., Providence, RI (1970), pp. 165-184

[4] Y. Matsuda, Diffeomorphism groups of the interval and periodic leaves of codimension one foliations, in preparation

[5] Y. Moriyama Polycyclic groups of diffeomorphisms on the half-line, Hokkaido Math. J., Volume 23 (1994) no. 3, pp. 399-422

[6] A. Navas Groupes résolubles de difféomorphismes de l'intervalle, du cercle et de la droite, Bull. Braz. Math. Soc. (N.S.), Volume 35 (2004) no. 1, pp. 13-50

[7] A. Navas Quelques groupes moyennables de difféomorphismes de l'intervalle, Bol. Soc. Mat. Mexicana, Volume 10 (2004), pp. 219-244

[8] J. Plante Solvable groups acting on the line, Trans. Amer. Math. Soc., Volume 278 (1983), pp. 401-414

[9] J. Plante Subgroups of continuous groups acting differentiably on the half-line, Ann. Inst. Fourier (Grenoble), Volume 34 (1984) no. 1, pp. 47-56

[10] J. Plante; W. Thurston Polynomial growth in holonomy groups of foliations, Comment. Math. Helv., Volume 51 (1976) no. 4, pp. 567-584

[11] M. Raghunathan Discrete Subgroups of Lie Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York–Heidelberg, 1972

[12] T. Tsuboi On the foliated products of class $C^{1}$ , Ann. of Math. (2), Volume 130 (1989) no. 2, pp. 227-271

[13] J. Wolf Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geom., Volume 2 (1968), pp. 421-446

Cited by Sources:

Comments - Policy