Factoring formal maps into reversible or involutive factors.

Abstract: An element g of a group is called reversible if it is conjugate in the group to its inverse. An element is an involution if it is equal to its inverse. This paper is about factoring elements as products of reversibles in the group of formal maps of , i.e. formally-invertible n-tuples of formal power series in n variables, with complex coefficients. The case was already understood [25]. Each product F of reversibles has linear part of determinant ±1. The main results are that for each map F with is the product of reversibles, and may also be factored as the product of involutions (where the ceiling of x is the smallest integer ⩾x). [Copyright &y& Elsevier]