10 citations · 11 across the 6 of their papers we have counts for
8 papers
Explicit linearization of multi-dimensional germs and vector fields through Ecalle's tree expansions
Frédéric Fauvet, Frédéric Menous, David Sauzin
We revisit the Siegel linearization problem by means of explicit formulas of non-recursive type for the linearizing transformations of a non-resonant holomorphic germ of diffeomorp…
Ecalle's paralogarithmic resurgence monomials and effective synthesis
Frederic Fauvet
Paralogarithms constitute a family of special functions, which are some generalizations of hyperlogarithms. They have been introduced by Jean Ecalle in the context of the classific…
Resurgence and holonomy of the model in zero dimension
Frédéric Fauvet, Frédéric Menous, Julien Quéva
We describe the resurgence properties of some partition functions corresponding to field theories in dimension 0. We show that these functions satisfy linear differential equations…
A comodule-bialgebra structure for word-series substitution and mould composition
Kurusch Ebrahimi-Fard, Frédéric Fauvet, Dominique Manchon
An internal coproduct is described, which is compatible with Hoffman's quasi-shuffle product. Hoffman's quasi-shuffle Hopf algebra, with deconcatenation coproduct, is a comodule-Ho…
Operads of finite posets
Frédéric Fauvet, Loïc Foissy, Dominique Manchon
We describe four natural operad structures on the vector space generated by isomorphism classes of finite posets. The three last ones are set-theoretical and can be seen as a simpl…
The Hopf algebra of finite topologies and mould composition
Frédéric Fauvet, Loïc Foissy, Dominique Manchon
We exhibit an internal coproduct on the Hopf algebra of finite topologies recently defined by the second author, C. Malvenuto and F. Patras, dual to the composition of "quasi-ormou…
Ecalle's arborification-coarborification transforms and Connes-Kreimer Hopf algebra
Frédéric Fauvet, Frederic Menous
We give a natural and complete description of Ecalle's mould-comould formalism within a Hopf-algebraic framework. The arborification transform thus appears as a factorization of ch…
Global behavior of solutions of nonlinear ODEs in $\CC$: first order equations
O. Costin, M. Huang, F. Fauvet
We show that the solutions of first order nonlinear ODEs can be controlled globally in the complex domain, using a finite set of constants of motion defined in regions of $\CC$. Th…