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

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.

Full text (pdf)

• Paweł Wilczyński
• Jagiellonian University, Faculty of Mathematics and Computer Science, Department of Applied Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland
• Revised: 2012-07-11.
• Accepted: 2012-07-18.