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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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Quadratic differential equations in the complex domain I
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by Nora C. Hopkins PDF
Trans. Amer. Math. Soc. 367 (2015), 6771-6782 Request permission

Abstract:

By complexifying all of the variables of an ordinary real quadratic vector differential equation to get a differential equation over $\mathbb {C}$, it is shown that the solution to the complex differential equation can be uniquely defined on an open star-shaped subset of $\mathbb {C}$, dependent on the initial point, containing the maximum interval of existence of the real differential equation. Complex conjugation is shown to commute with solving the differential equation on this complex domain, and well-known algebraic properties of the solutions to the real differential equation are generalized to the equation over $\mathbb {C}$.
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Additional Information
  • Nora C. Hopkins
  • Affiliation: Department of Mathematics and Computer Science, Indiana State University, Terre Haute, Indiana 47809
  • MR Author ID: 217047
  • Received by editor(s): March 11, 2009
  • Published electronically: June 16, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 6771-6782
  • MSC (2010): Primary 34M99, 34C14, 17A36
  • DOI: https://doi.org/10.1090/tran/5318
  • MathSciNet review: 3378813