On the sharp regularity for arbitrary actions of nilpotent groups on the interval: the case of N_4

TL;DR

This paper identifies the maximal regularity class for which a specific nilpotent group of 4x4 integer matrices can act smoothly on the closed interval.

Contribution

It precisely determines the largest  for which the 4x4 nilpotent matrix group embeds into C1+ diffeomorphisms of the interval.

Findings

Identifies the maximal  for embedding the group into smooth interval diffeomorphisms.

Provides a sharp regularity threshold for group actions on the interval.

Advances understanding of nilpotent group actions in smooth dynamics.

Abstract

We determine the largest {\alpha} for which the nilpotent group of 4-by-4 triangular matrices with integer coefficients and 1 in the diagonal embeds into the group of C1+{\alpha} diffeomorphism of the closed interval.