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

2024/06/17 by Opazo, Leonardo Dinamarca, Navas, Andrés · 1 citation
#37C05 #37C10 #37C15 #37C85 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2406.11587

Abstract

We consider C² 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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• Almost reducibility, distortion and local perfection for diffeomorphisms of one-manifolds

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