Growth of Groups and Diffeomorphisms of the Interval
. We prove that, for all α > 0, every finitely generated group of C 1+ α diffeomorphisms of the interval with sub-exponential growth is almost nilpotent. Consequently, there is no group of C 1+ α interval diffeomorphisms having intermediate growth. In addition, we show that the C 1+ α regularity...
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| Veröffentlicht in: | Geometric and functional analysis 2008-09, Vol.18 (3), p.988-1028 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | .
We prove that, for all
α
> 0, every finitely generated group of
C
1+
α
diffeomorphisms of the interval with sub-exponential growth is almost nilpotent. Consequently, there is no group of
C
1+
α
interval diffeomorphisms having intermediate growth. In addition, we show that the
C
1+
α
regularity hypothesis for this assertion is essential by giving a
C
1
counter-example. |
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| ISSN: | 1016-443X 1420-8970 |
| DOI: | 10.1007/s00039-008-0667-6 |