D-log and formal flow for analytic isomorphisms of n-space

Details D-log and formal flow for analytic isomorphisms of n-space D-log and formal flow for analytic isomorphisms of n-space

2002-09-20

arxiv.org/abs/math/0209274v1

Trans. Amer. Math. Soc. 355 (2003), No. 8, 3117-3141.

Mathematics

Complex Variables

Latex, 32 pages

Scientific paper

Given a formal map $F=(F_1...,F_n)$ of the form $z+\text{higher}$ order terms, we give tree expansion formulas and associated algorithms for the D-Log of F and the formal flow F_t. The coefficients which appear in these formulas can be viewed as certain generalizations of the Bernoulli numbers and the Bernoulli polynomials. Moreover the coefficient polynomials in the formal flow formula coincide with the strict order polynomials in combinatorics for the partially ordered sets induced by trees. Applications of these formulas to the Jacobian Conjecture are discussed.

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