Planar nonautonomous polynomial equations V. The Abel equation

• Autorzy: Wilczyński P.
• Języki publikacji: EN

Abstrakty

EN

We give a full description of the dynamics of the Abel equation [formula] for some special complex valued ƒ. We also prove the existence of at least three periodic solutions for equations of the form [formula] for odd n ≥ 5.

Słowa kluczowe

EN

periodic orbits; polynomial equations

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 1
• Strony: 175--189
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Wilczyński P.

• Jagiellonian University, Faculty of Mathematics and Computer Science, Department of Applied Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland,

Bibliografia

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• [2] A. Lins Neto, On the number of solutions of the equation dx/dt = ^2"=0 cij{t)x\ 0 < t < 1, for which x(0) = x(l), Invent. Math. 59 (1980) 1, 67-76.
• [3] A.A. Panov, Variety of Poincare mappings for cubic equations with variable coefficients. Funktsional. Anal, i Prilozhen. 33 (1999) 4, 84-88.
• [4] P. Wilczynski, Planar nonautonomous polynomial equations III. Zeroes of the vector field. accepted in Topol. Methods Nonlinear Anal.
• [5] P. Wilczynski, Periodic solutions of polynomial planar nonautonomous equations, Ital. J. Pure Appl. Math. 21 (2007), 235-250.
• [6] P. Wilczynski, Planar nonautonomous polynomial equations: the Riccati equation. J. Differential Equations 244 (2008) 6, 1304-1328.
• [7] P. Wilczynski, Planar nonautonomous polynomial equations. II. Coinciding sectors. J. Differential Equations 246 (2009) 7, 2762-2787.
• [8] H. Zoladek. Periodic planar systems without periodic solutions, Qual. Theory Dyn. Syst. 2 (2001) 1, 45-60.