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 (Original language)
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

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     title = {Polycyclic groups of diffeomorphisms of the closed interval},
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     doi = {10.1016/j.crma.2009.04.008},
     language = {en},
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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

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