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

Wright, David; Zhao, Wenhua

doi:10.1090/S0002-9947-03-03295-1

D-log and formal flow for analytic isomorphisms of n-space
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by David Wright and Wenhua Zhao PDF

Trans. Amer. Math. Soc. 355 (2003), 3117-3141 Request permission

Abstract:

Given a formal map $F=(F_1,\ldots ,F_n)$ 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 that 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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