Opuscula Math. 30, no. 1 (2010), 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
Piotr Oprocha
Paweł Wilczyński
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.
- Piotr Oprocha
- Universidad de Murcia, Departamento de Matemáticas, Campus de Espinardo, 30100 Murcia, Spain
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
- Paweł Wilczyński
- Jagiellonian University, Institute of Mathematics, ul. Łojasiewicza 6, 30-348 Kraków, Poland
- Received: 2009-04-11.
- Revised: 2009-10-05.
- Accepted: 2009-10-14.
