arXiv subjects
Publications and source records attributed to Paweł Wilczyński.
We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of infinitely many heteroclinic solutions betwen the periodic ones.
The main aim of this article is to show that maps with specification property have invariant distributionally scrambled sets and that this kind of scrambled set can be transferred from factor to extension under finite-to-one factor maps. This solves some open questions in the literature of the topic. We also show how our method can be applied in practice, taking as example Poincaré map of time-periodic nonautonomous planar differential equation $$ \dot{z}=v(t,z)=(1+e^{iκt}\abs{z}^2)\z^3 -N $$ where $κ$ and $N$ are sufficiently small positive real numbers.