Exact quadratic growth for the derivatives of iterates of interval diffeomorphisms with only parabolic fixed points

Abstract

We consider $C^2$ diffeomorphisms of a closed interval with only parabolic fixed points. We show that the maximal growth of the derivatives of the iterates of such a diffeomorphism is exactly quadratic provided it has a non-quadratical tangency to the identity at a fixed point that is topologically repelling on one side. Moreover, in absence of such fixed points, the maximal growth of the derivatives of the iterates is subquadratic.

Some minor changes. To appear