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Bifurcation of the periodic differential equations with regularisable infinity

Published online by Cambridge University Press:  14 November 2011

Guan Ke-ying
Department of Mathematics, Beijing Institute of Aeronautics and Astronautics, P.O. Box 85, Beijing, PR China


A class of scalar periodic differential equations x ]f(x, t, A) with regularisable infinity in which the Riccati equation is included, can be treated as autonomous systems on the torus T2. Through this geometric interpretation, the properties of the set of bifurcation points of λ (∊R) are studied. When the results obtained are applied to the Riccati equation, they can match the well-known properties of the spectral set of the corresponding Hill's equation.

Research Article
Copyright © Royal Society of Edinburgh 1987

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