Opuscula Math. 33, no. 1 (2013), 175-189

Opuscula Mathematica

Planar nonautonomous polynomial equations V. The Abel equation

Paweł Wilczyński

Abstract. We give a full description of the dynamics of the Abel equation \(\dot{z}=z^3+f(t)\) for some special complex valued \(f\). We also prove the existence of at least three periodic solutions for equations of the form \(\dot{z}=z^n+f(t)\) for odd \(n \geq 5\).

Keywords: periodic orbits, polynomial equations.

Mathematics Subject Classification: 34C25, 34C37.

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  • Paweł Wilczyński
  • Jagiellonian University, Faculty of Mathematics and Computer Science, Department of Applied Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland
  • Received: 2012-05-15.
  • Revised: 2012-07-11.
  • Accepted: 2012-07-18.
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Cite this article as:
Paweł Wilczyński, Planar nonautonomous polynomial equations V. The Abel equation, Opuscula Math. 33, no. 1 (2013), 175-189, http://dx.doi.org/10.7494/OpMath.2013.33.1.175

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