`a`
Journal of Modern Dynamics (JMD)
 

Growth gap versus smoothness for diffeomorphisms of the interval

Pages: 629 - 643, Issue 4, October 2008      doi:10.3934/jmd.2008.2.629

 
       Abstract        Full Text (143.0K)       Related Articles

Lev Buhovski - School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel (email)
Roman Muraviev - School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Israel (email)

Abstract: 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.

Keywords:  Growth sequences, growth gap, diffeomorphisms of the interval
Mathematics Subject Classification:  37C05, 37E05

Received: February 2008;      Revised: July 2008;      Available Online: October 2008.