TY  - JOUR
ID  - Oprocha2010
LB  - Oprocha2010
AU  - Oprocha, Piotr
AU  - Wilczyński, Paweł
TI  - A study of chaos for processes under small perturbations II: rigorous proof of chaos
ST  - A study of chaos for processes under small perturbations II: rigorous proof of chaos
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 1
SP  - 5
EP  - 36
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.1.5
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.1.5
AB  - 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.
KW  - distributional chaos
KW  - isolating segments
KW  - fixed point index
KW  - bifurcation
SN  - 1232-9274
ER  -