Opuscula Mathematica
Opuscula Math. 30, no. 1 (), 5-36
http://dx.doi.org/10.7494/OpMath.2010.30.1.5
Opuscula Mathematica

A study of chaos for processes under small perturbations II: rigorous proof of chaos



Abstract. In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation \[\dot{z}=\left(1 + e^{i\kappa t} |z|^2\right)\bar{z}^2 - N e^{-i\frac{\pi}{3}}.\] Heteroclinic and homoclinic connections between two periodic solutions bifurcating from the stationary solution \(0\) present in the system when \(N = 0\) are also discussed.
Keywords: distributional chaos, isolating segments, fixed point index, bifurcation.
Mathematics Subject Classification: 34C28, 37B30.
Cite this article as:
Piotr Oprocha, Paweł Wilczyński, A study of chaos for processes under small perturbations II: rigorous proof of chaos, Opuscula Math. 30, no. 1 (2010), 5-36, http://dx.doi.org/10.7494/OpMath.2010.30.1.5
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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