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On the sharp regularity for arbitrary actions of nilpotent groups on the interval: the case of $N_{4}$

Published online by Cambridge University Press:  28 July 2016

EDUARDO JORQUERA ,
ANDRÉS NAVAS  and
CRISTÓBAL RIVAS
EDUARDO JORQUERA
Affiliation:
Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile email [email protected]
ANDRÉS NAVAS
Affiliation:
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Alameda 3363, Estación Central, Santiago, Chile email [email protected], [email protected]
CRISTÓBAL RIVAS
Affiliation:
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Alameda 3363, Estación Central, Santiago, Chile email [email protected], [email protected]
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Abstract

In this work, we determine the largest $\unicode[STIX]{x1D6FC}$ for which the nilpotent group of four-by-four triangular matrices with integer coefficients and the value one in the diagonal embeds into the group of $C^{1+\unicode[STIX]{x1D6FC}}$ diffeomorphisms of the closed interval.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 1 , February 2018 , pp. 180 - 194
Copyright
© Cambridge University Press, 2016 

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