Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Czasopismo
Rocznik
Tom
Numer
Strony
159-168
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-31
poprawiono
1999-10-20
Twórcy
autor
- Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Bibliografia
- [Ma] J. Mawhin, Periodic solutions of some planar non-autonomous polynomial differential equations, J. Differential Integral Equations 7 (1994), 1055-1061.
- [MMZ] R. Manásevich, J. Mawhin and F. Zanolin, Periodic solutions of complex-valued differential equations and systems with periodic coefficients, J. Differential Equations 126 (1996), 355-373.
- [MM] K. Mischaikow and M. Mrozek, Chaos in Lorenz equations: a computer assisted proof, Bull. Amer. Math. Soc. 32 (1995), 66-72.
- [S] R. Srzednicki, Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations, Nonlinear Anal. 22 (1994), 707-737.
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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