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.