Non-autonomous equations related to polynomial two-dimensional systems
Authors:
- 1 January 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 105 (1) , 129-152
Abstract
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.Keywords
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