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26.—Singularities of Solutions of Certain Plane Autonomous Systems

Published online by Cambridge University Press:  14 February 2012

Russell A. Smith
Russell A. Smith
Affiliation:
Department of Mathematics, University of Durham.
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Extract

The paper discusses the nature of the singularities at any finite point t = t0 of real solutions x(t), y(t) of the system of differential equations x′ = P(x, y), y′ = Q(x, y) in which P, Q are polynomials in both x and y. Its main interest is in cases when the leading terms of P, Q are of the same degree n. Conditions are given under which the only possible singularities are algebraic poles and pseudo-poles. Conditions are also given under which the only possible singularities are of wildly oscillatory type.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 72 , Issue 4 , 1975 , pp. 307 - 315
Copyright
Copyright © Royal Society of Edinburgh 1975

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References

References to Literature

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