@Article{Oprocha2010,
author = "Oprocha, Piotr and Wilczyński, Paweł",
title = "A study of chaos for processes under small perturbations II: rigorous proof of chaos",
journal = "Opuscula Math.",
year = "2010",
volume = "30",
number = "1",
pages = "5--36",
doi = "http://dx.doi.org/10.7494/OpMath.2010.30.1.5",
url = "http://dx.doi.org/10.7494/OpMath.2010.30.1.5",
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",
issn = "1232-9274"
}