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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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
  • Received by editor(s): June 5, 2002
  • Received by editor(s) in revised form: January 3, 2003
  • Published electronically: April 14, 2003
  • © Copyright 2003 American Mathematical Society
  • 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
  • MathSciNet review: 1974678