# Chaos in some planar nonautonomous polynomial differential equation

Annales Polonici Mathematici (2000)

- Volume: 73, Issue: 2, page 159-168
- ISSN: 0066-2216

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topWójcik, Klaudiusz. "Chaos in some planar nonautonomous polynomial differential equation." Annales Polonici Mathematici 73.2 (2000): 159-168. <http://eudml.org/doc/262600>.

@article{Wójcik2000,

abstract = {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.},

author = {Wójcik, Klaudiusz},

journal = {Annales Polonici Mathematici},

keywords = {periodic solutions; fixed point index; Lefschetz number; chaos; chaotic dynamics; Lefschetz fixed point theorem; Ważewski retract theorem; isolating segment; Poincaré map},

language = {eng},

number = {2},

pages = {159-168},

title = {Chaos in some planar nonautonomous polynomial differential equation},

url = {http://eudml.org/doc/262600},

volume = {73},

year = {2000},

}

TY - JOUR

AU - Wójcik, Klaudiusz

TI - Chaos in some planar nonautonomous polynomial differential equation

JO - Annales Polonici Mathematici

PY - 2000

VL - 73

IS - 2

SP - 159

EP - 168

AB - 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.

LA - eng

KW - periodic solutions; fixed point index; Lefschetz number; chaos; chaotic dynamics; Lefschetz fixed point theorem; Ważewski retract theorem; isolating segment; Poincaré map

UR - http://eudml.org/doc/262600

ER -

## References

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- [S1] R. Srzednicki, On periodic solutions of planar differential equations with periodic coefficients, J. Differential Equations 114 (1994), 77-100. Zbl0811.34031
- [SW] R. Srzednicki and K. Wójcik, A geometric method for detecting chaotic dynamics, ibid. 135 (1997), 66-82. Zbl0873.58049
- [W] S. Wiggins, Global Bifurcation and Chaos. Analytical Methods, Springer, New York, 1988. Zbl0661.58001
- [W1] K. Wójcik, Isolating segments and symbolic dynamics, Nonlinear Anal. 33 (1998), 575-591. Zbl0955.37005
- [W2] K. Wójcik, On detecting periodic solutions and chaos in ODE's, ibid., to appear.

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