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By José Manuel Aroca, Ragnar Buchweitz, Marc Giusti, Michel Merle (Editors)

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Mq~s -1 we get simple i = 0,. ,hi (take q free points 0q i > O. i The 0 0 = O. i position and h ~ points~ we m e a n and each = ~ ) is the the i = The have with exponent 0 J0 a free the in relationship to t h e p r e c e e d i n 9 it an of in the Puiseux series. is Here b y characteristic indetermination. ~ have a [1] until the partial sum branches Then in in the unity. In way that root of such a is a. -th J y' y' point series ~-1' corresponding is a.. c~J through series OJi' j=O, . . , which point determined~ coefficient O.

X' Remark. The satellitism linear O' that 01 of the transformation at 01 to and see the the following to y' x', y'/x' that rings = @ O. are can C[[x,y/x]] be and computation [ b i , J. x ' i+j ( y ' / x ' ~j assume corresponds 1 between )J may i+j-1 (y '/x' )J x ' i+j-1 (y ' / x ' )J ~:ai~j / + ... denominator intrinsic guarantees points we suffices isomorphism 'J" last satellite Now 1" a parameters b i , j x ' l Y• the lemma Then local an this = (bo,1/al,0)(Y'/X') since O' the performing are at extended C[[x'~y'/x']] of y parameters uniquely part into is a u n i t character that the satellite in C [ [ x ' ~ y ' / x ' ] ] .

2. For rational We call Then each admissible we F. sequences of values of have positive function the in integer 2i + n - i such that i m + 1 variables + n ~/ I" t h e r e such that I F i ( X0, • • • ~ X i _ l , b 0 , • • • ~bi+n_m ) is defined a i) are for We admissible sequences of b's Xi = F i ( x 0 , . . , X i _ l , b 0 , . . , b i + n _ necessary Proof. each and will sufficient assume m) conditions that by in an , order and X's and i + n ~/I" that inductive ~p(x) £ R 2. process we have 51 constructed rational expression Hi ( ~ , 0 , .

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