Growth Gap vs. smoothness for diffeomorphisms of the interval

Details Growth Gap vs. smoothness for diffeomorphisms of the interval Growth Gap vs. smoothness for diffeomorphisms of the interval

2008-02-26

arxiv.org/abs/0802.3930v2

Journal of Modern Dynamics, Volume 2, No. 4, 629--643, 2008

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3934/jmd.2008.2.629

Given a diffeomorphism of the interval, consider the uniform norm of the derivative of its n-th iteration. We get a sequence of real numbers called the growth sequence. Its asymptotic behavior is an invariant which naturally appears both in smooth dynamics and in geometry of the diffeomorphisms groups. We find sharp estimates for the growth sequence of a given diffeomorphism in terms of the modulus of continuity of its derivative. These estimates extend previous results of Polterovich and Sodin, and Borichev.

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