Ascertaining when a basin is Wada: the merging method
Chaotic Dynamics
2018-06-19 v2
Abstract
Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under the action of merging the basins. This observation allows to develop a new method to test the Wada property, which is much faster than the previous ones. Furthermore, another major advantage of the merging method is that a detailed knowledge of the dynamical system is not required.
Cite
@article{arxiv.1803.03480,
title = {Ascertaining when a basin is Wada: the merging method},
author = {Alvar Daza and Alexandre Wagemakers and Miguel A. F. Sanjuán},
journal= {arXiv preprint arXiv:1803.03480},
year = {2018}
}