A study of chaos for processes under small perturbations II - rigorous proof of chaos - Oprocha, Piotr; Wilczyński, Paweł (My University, 2010)
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.
Opuscula Mathematica
Keywords: distributional chaos; isolating segments; fixed point index; bifurcation