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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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Generalized Toda flows
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by Darren C. Ong and Christian Remling PDF
Trans. Amer. Math. Soc. 371 (2019), 5069-5081 Request permission


The classical hierarchy of Toda flows can be thought of as an action of the (abelian) group of polynomials on Jacobi matrices. We present a generalization of this to the larger groups of $C^2$ and entire functions, and in this second case, we also introduce associated cocycles and in fact give center stage to this object.
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Additional Information
  • Darren C. Ong
  • Affiliation: Department of Mathematics, Xiamen University Malaysia, Jalan Sunsuria, Bandar Sunsuria, 43900 Sepang, Selangor Darul Ehsan, Malaysia
  • MR Author ID: 845285
  • Email:
  • Christian Remling
  • Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
  • MR Author ID: 364973
  • Email:
  • Received by editor(s): February 4, 2018
  • Received by editor(s) in revised form: July 15, 2018
  • Published electronically: November 13, 2018
  • Additional Notes: The first author was supported by a Xiamen University Malaysia Research Fund (Grant No. XMUMRF/2018-C1/IMAT/0001).
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 5069-5081
  • MSC (2010): Primary 34L40, 37K10, 47B36, 81Q10
  • DOI:
  • MathSciNet review: 3934478