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 invariantwhich 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 diffeomorphismin terms of themodulus of continuity of its derivative. These estimates extend previous results of Polterovich-Sodin and Borichev.
- Diffeomorphisms of the interval
- Growth gap
- Growth sequences