# Intertwined mappings

@inproceedings{calle2006IntertwinedM,
title={Intertwined mappings},
author={Jean {\'E}calle},
year={2006}
}
We show that, contrary to expectations, there exist pairs of formal and even analytic, non-commuting and non-elementary (neither algebraic nor algebraic-differential) mapping germs in Diff(C, 0) that are ‘entwined’ in a group relation W (f, g) = id. In the case of identity-tangent mappings, ‘twins’ exhibit, rather than analyticity, generic divergence , but of a particularly interesting sort : resurgent, accelero-summable, and with simple alien derivatives.
3 Citations
• Mathematics
Compositio Mathematica
• 2013
Abstract We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0\in \mathbb{C}$ is free in the sense of pseudogroups even if the class of conjugacy of the
• Mathematics
• 2010
A word of germs of holomorphic diffeomorphisms of (C, 0) is a composite of some time-1 maps of formal vector fields fixing 0, in other words, a noncommutative integral of a piecewise constant time
We study the structure of discrete subgroups of the group $G[[r]]$ of complex formal power series under the operation of composition of series. In particular, we prove that every finitely generated

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