English

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 C2C^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.

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