Initiation to mould calculus through the example of saddle-node singularities

Details Initiation to mould calculus through the example of saddle-node singularities Initiation to mould calculus through the example of saddle-node singularities

2007-12-29

arxiv.org/abs/0801.0073v2

Mathematics

Dynamical Systems

13 pages. A para\^itre dans Rev. Semin. Iberoam. Mat. Singul. Tordesillas

Scientific paper

This article proposes an initiation to \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field. This is illustrated on the case of saddle-node singularities, generated by two-dimensional vector fields which are formally conjugate to Euler's vector field $x^2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$, and for which the formal normalisation proves to be resurgent in $1/x$.

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