Intertwined mappings

  title={Intertwined mappings},
  author={Jean {\'E}calle},
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. 

Generic pseudogroups on $( \mathbb{C} , 0)$ and the topology of leaves

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

Relations of Formal Diffeomorphisms and the Center Problem

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

Subgroups of the Group of Formal Power Series with the Big Powers Condition

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



Six Lectures on Transseries, Analysable Functions and the Constructive Proof of Dulac’s Conjecture

The present paper gives a rapid, self-contained introduction to some new resummotion methods, which are noticeable for their high content in structure and revolve logically around the notions of

Complex transseries solutions to algebraic differential equations

This paper shows how to determine the solutions of an arbitrary algebraic differential equation over the complex transseries, and shows that such equations always admit complex trans series solutions.

Ecole Polytechnique, Fr

  • 1997

SD.), Glass (A.M.W)

  • Bull. Austral. Math. Soc. 51,
  • 1995