Abstract.
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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Received: November 2006, Revised: July 2007, Accepted: July 2007
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Navas, A. Growth of Groups and Diffeomorphisms of the Interval. GAFA Geom. funct. anal. 18, 988–1028 (2008). https://doi.org/10.1007/s00039-008-0667-6
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DOI: https://doi.org/10.1007/s00039-008-0667-6