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D-log and formal flow for analytic isomorphisms of n-space | | David Wright
; Wenhua Zhao
; | | Date: |
20 Sep 2002 | | Subject: | Complex Variables; Combinatorics MSC-class: Primary 14R10, 11B68; Secondary 14R15, 05C05 | math.CV math.CO | | Abstract: | Given a formal map $F=(F_1...,F_n)$ of the form $z+ ext{higher}$ 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. | | Source: | arXiv, math.CV/0209274 | | Services: | Forum | Review | PDF | Favorites | |
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