Opuscula Math. 33, no. 1 (2013), 175-189
http://dx.doi.org/10.7494/OpMath.2013.33.1.175
Opuscula Mathematica
Planar nonautonomous polynomial equations V. The Abel equation
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.
- 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.
