Exact quadratic growth for the derivatives of iterates of interval diffeomorphisms with only parabolic fixed points
Dynamical Systems
2024-11-12 v2 Functional Analysis
Geometric Topology
Abstract
We consider 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.
Keywords
Cite
@article{arxiv.2406.11587,
title = {Exact quadratic growth for the derivatives of iterates of interval diffeomorphisms with only parabolic fixed points},
author = {Leonardo Dinamarca Opazo and Andrés Navas},
journal= {arXiv preprint arXiv:2406.11587},
year = {2024}
}
Comments
Some minor changes. To appear