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Growth gap versus smoothness for diffeomorphisms of the interval

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  • Given a diffeomorphism of the interval, we 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 the geometry of the diffeomorphism group. 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--Sodin and Borichev.
    Mathematics Subject Classification: 37C05, 37E05.


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