Intertwined mappings
نویسندگان
چکیده
— 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. RÉSUMÉ. — Nous montrons que, contrairement à une attente assez partagée, il existe dans Diff(C, 0) des paires (f, g) de difféos locaux jumelés, qui engendrent des groupes « intéressants », i.e. ni libres ni trop élémentaires (ils ne sont pas abéliens et ne se réduisent pas, même après éclatement, à des groupes d’homographies). De tels groupes sont dits liés. Nous ébauchons une classification des relations W (f, g), nécessairement très sporadiques, qui les définissent. Dans le cas de difféos tangents à l’identité, les générateurs jumelés f, g sont génériquement divergents, mais résurgents, accéléro-sommables, et ils possèdent des dérivées étrangères remarquables.
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