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Examples of distorted interval diffeomorphisms of intermediate regularity

Part of: Low-dimensional dynamical systems Smooth dynamical systems: general theory Special aspects of infinite or finite groups

Published online by Cambridge University Press:  08 September 2021

LEONARDO DINAMARCA  and
MAXIMILIANO ESCAYOLA
LEONARDO DINAMARCA*
Affiliation:
Departamento de Matemática y Ciencias de la Computación, Universidad de Santiago de Chile (USACH), Alameda Libertador Bernardo O’Higgins 3363, Estación Central, Santiago, Chile (e-mail: maximiliano.escayola@usach.cl)
MAXIMILIANO ESCAYOLA
Affiliation:
Departamento de Matemática y Ciencias de la Computación, Universidad de Santiago de Chile (USACH), Alameda Libertador Bernardo O’Higgins 3363, Estación Central, Santiago, Chile (e-mail: maximiliano.escayola@usach.cl)
*
e-mail: leonardo.dinamarca@usach.cl
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Abstract

We improve a recent construction of Andrés Navas to produce the first examples of $C^2$ -undistorted diffeomorphisms of the interval that are $C^{1+\alpha }$ -distorted (for every ${\alpha < 1}$ ). We do this via explicit computations due to the failure of an extension to class $C^{1+\alpha }$ of a classical lemma related to the work of Nancy Kopell.

Keywords

interval diffeomorphismHölder continuitydistorted elementdistortion

MSC classification

Primary: 20F99: None of the above, but in this section 37C05: Smooth mappings and diffeomorphisms 37C85: Dynamics of group actions other than ${bf Z}$ and ${bf R}$, and foliations 37E05: Maps of the interval (piecewise continuous, continuous, smooth)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 11 , November 2022 , pp. 3311 - 3324
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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