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arXiv · 2406.11587

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

Leonardo Dinamarca Opazo·Andrés Navas
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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.

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Leonardo Dinamarca Opazo, Andrés Navas. 2024-06-17. Exact quadratic growth for the derivatives of iterates of interval diffeomorphisms with only parabolic fixed points. https://arxiv.org/abs/2406.11587

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