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. 

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