Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

Quadratic differential equations in the complex domain I


Author: Nora C. Hopkins
Journal: Trans. Amer. Math. Soc. 367 (2015), 6771-6782
MSC (2010): Primary 34M99, 34C14, 17A36
DOI: https://doi.org/10.1090/tran/5318
Published electronically: June 16, 2015
MathSciNet review: 3378813
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 34M99, 34C14, 17A36

Retrieve articles in all journals with MSC (2010): 34M99, 34C14, 17A36


Additional Information

Nora C. Hopkins
Affiliation: Department of Mathematics and Computer Science, Indiana State University, Terre Haute, Indiana 47809

DOI: https://doi.org/10.1090/tran/5318
Received by editor(s): March 11, 2009
Published electronically: June 16, 2015
Article copyright: © Copyright 2015 American Mathematical Society