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Periodic planar systems without periodic solutions

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Abstract

We construct examples of non-autonomous planar systems of the formdz/dt=z n+p n−1(e it)z n−1+…+p 0(e it),p j —polynomials, which do not have periodic solutions. For the Riccati systemdz/dt=z 2+re it we express the valuesr j of the parameter for which there is no periodic solution by means of zeroes of some Bessel function.

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Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Henryk Żołądek

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  1. Henryk Żołądek
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Correspondence to Henryk Żołądek.

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Submitted by J.P. Françoise

The work was supported by the Polish KBN Grant No 2 P03A 041 15

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Żołądek, H. Periodic planar systems without periodic solutions. Qual. Th. Dyn. Syst. 2, 45–60 (2001). https://doi.org/10.1007/BF02969380

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