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Non-autonomous equations related to polynomial two-dimensional systems

Published online by Cambridge University Press:  14 November 2011

M. A. M. Alwash  and
N. G. Lloyd
M. A. M. Alwash
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth, Dyfed, Wales
N. G. Lloyd
Affiliation:
Department of Mathematics, The University College of Wales, Aberystwyth, Dyfed, Wales
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Synopsis

Periodic solutions of certain one-dimensional non-autonomous differential equations are investigated (equation (1.4)); the independent variable is complex. The motivation, which is explained in the introductory section, is the connection with certain polynomial two-dimensional systems. Several classes of coefficients are considered; in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. In particular, we need to know when there is a full neighbourhood of periodic solutions. We give a number of sufficient conditions and investigate the implications for the corresponding two-dimensional systems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 129 - 152
Copyright
Copyright © Royal Society of Edinburgh 1987

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