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


Authors: David Wright and Wenhua Zhao
Journal: Trans. Amer. Math. Soc. 355 (2003), 3117-3141
MSC (2000): Primary 14R10, 11B68; Secondary 14R15, 05C05
DOI: https://doi.org/10.1090/S0002-9947-03-03295-1
Published electronically: April 14, 2003
MathSciNet review: 1974678
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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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Additional Information

David Wright
Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130-4899
Email: wright@einstein.wustl.edu

Wenhua Zhao
Affiliation: Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130-4899
Email: zhao@math.wustl.edu

DOI: https://doi.org/10.1090/S0002-9947-03-03295-1
Keywords: D-log, formal flow of automorphisms, rooted trees, order polynomials, Bernoulli numbers and polynomials
Received by editor(s): June 5, 2002
Received by editor(s) in revised form: January 3, 2003
Published electronically: April 14, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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