American Institute of Mathematical Sciences

October  2008, 2(4): 629-643. doi: 10.3934/jmd.2008.2.629

Growth gap versus smoothness for diffeomorphisms of the interval

 1 School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel, Israel

Received  February 2008 Revised  July 2008 Published  October 2008

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.
Citation: Lev Buhovski, Roman Muraviev. Growth gap versus smoothness for diffeomorphisms of the interval. Journal of Modern Dynamics, 2008, 2 (4) : 629-643. doi: 10.3934/jmd.2008.2.629
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