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On Periodic Solutions of the Periodic

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Abstract

By treating the periodic Riccati equation

${\rm\dot{z}=a(t)z^2+b(t)z+c(t)}$

as a dynamical system on the sphere S, the number and stability of its periodic solutions are determined. Using properties of Moebius transformations, an exact algebraic relation is obtained between any periodic solution and any complex-valued periodic solution. This leads to a new method for constructing the periodic solutions.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Birmingham/England, England

    K. Y. Guan, J. Gunson & H. S. Hassan

Authors
  1. K. Y. Guan
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  2. J. Gunson
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  3. H. S. Hassan
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Additional information

On leave from the Institute of Aeronautics and Astronautics, Beijing, P.R. China.

On leave from the University of Qatar, Doha, Qatar.

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Guan, K.Y., Gunson, J. & Hassan, H.S. On Periodic Solutions of the Periodic. Results. Math. 14, 309–317 (1988). https://doi.org/10.1007/BF03323232

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  • DOI: https://doi.org/10.1007/BF03323232

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