arXiv subjects

Leonardo Dinamarca Opazo

Publications and source records attributed to Leonardo Dinamarca Opazo.

2 recordsLinked to original sources

arXiv2024

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

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.

math.DS↗

arXiv2024

Distortion in groups of generalized piecewise-linear transformations

For each natural number $n$, we consider the subgroup $\mathcal{R}_n$ of Homeo$_+[0,1]$ made by the elements that are linear except for a subset whose Cantor-Bendixson rank is less than or equal to $n$. These groups of generalized piecewise-linear transformations yield an ascending chain of groups as we increase $n$. We study how the notion of distorted element changes along this chain. Our main result establishes that for each natural number $n$, there exits an element that is undistorted of $\mathcal{R}_n$ yet distorted in $\mathcal{R}_{n+1}$. Actually, such an element is explicitly constructed.

math.GR↗