Periodic Planar Systems without Periodic Solutions

• Autores: Henryk Zoladek
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 2, Nº 1, 2001, págs. 45-60
• Idioma: español
• DOI: 10.1007/bf02969380
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• Resumen

  • We construct examples of non-autonomous planar systems of the form $ dz/dt=z^{n}+p_{n-1}(e^{it})z^{n-1}+\ldots +p_{0}(e^{it}),\;p_{j}$ -- polynomials, which do not have periodic solutions. For the Riccati system $dz/dt=z^{2}+re^{it}$ we express the values $r_{j}$ of the parameter for which there is no periodic solution by means of zeroes of some Bessel function