Chaos in some planar nonautonomous polynomial differential equation

• Autorzy: Klaudiusz Wójcik
• Języki publikacji: EN

Abstrakty

EN

We show that under some assumptions on the function f the system $ż = z̅(f(z) e^{iϕt} + e^{i2ϕt})$ generates chaotic dynamics for sufficiently small parameter ϕ. We use the topological method based on the Lefschetz fixed point theorem and the Ważewski retract theorem.

Słowa kluczowe

EN

periodic solutions; fixed point index; Lefschetz number; chaos

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2000
• Tom: 73
• Numer: 2
• Strony: 159-168

Daty

wydano

2000

otrzymano

1999-05-31

poprawiono

1999-10-20

Twórcy

autor

Klaudiusz Wójcik

• Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland

Bibliografia

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• [S1] R. Srzednicki, On periodic solutions of planar differential equations with periodic coefficients, J. Differential Equations 114 (1994), 77-100.
• [SW] R. Srzednicki and K. Wójcik, A geometric method for detecting chaotic dynamics, ibid. 135 (1997), 66-82.
• [W] S. Wiggins, Global Bifurcation and Chaos. Analytical Methods, Springer, New York, 1988.
• [W1] K. Wójcik, Isolating segments and symbolic dynamics, Nonlinear Anal. 33 (1998), 575-591.
• [W2] K. Wójcik, On detecting periodic solutions and chaos in ODE's, ibid., to appear.