Mould expansions for the saddle-node and resurgence monomials TeX Export

@misc{citeulike:2136042, abstract = {This article is an introduction to some aspects of \'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 or of map. This is illustrated on the case of the saddle-node, a two-dimensional vector field which is 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 is shown to be resurgent in \$1/x\$. Resurgence monomials adapted to alien calculus are also described as another application of mould calculus.}, archivePrefix = {arXiv}, author = {Sauzin, David}, citeulike-article-id = {2136042}, citeulike-linkout-0 = {http://arxiv.org/abs/0712.2337}, citeulike-linkout-1 = {http://arxiv.org/pdf/0712.2337}, day = {14}, eprint = {0712.2337}, keywords = {divergence, formal\_theory, normal\_forms}, month = {Dec}, posted-at = {2007-12-17 11:56:35}, priority = {3}, title = {Mould expansions for the saddle-node and resurgence monomials}, url = {http://arxiv.org/abs/0712.2337}, year = {2007} }

TY - ELEC ID - citeulike:2136042 L3 - citeulike-article-id:2136042 N2 - This article is an introduction to some aspects of \'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 or of map. This is illustrated on the case of the saddle-node, a two-dimensional vector field which is 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 is shown to be resurgent in $1/x$. Resurgence monomials adapted to alien calculus are also described as another application of mould calculus. TI - Mould expansions for the saddle-node and resurgence monomials KW - divergence KW - formal_theory KW - normal_forms AU - Sauzin, David PY - 2007/Dec/14/ UR - http://arxiv.org/abs/0712.2337 ER -