Ascertaining when a basin is Wada: the merging method

Alvar Daza; Alexandre Wagemakers; Miguel A. F. Sanjuán

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arXiv · 1803.03480

Ascertaining when a basin is Wada: the merging method

Alvar Daza·Alexandre Wagemakers·Miguel A. F. Sanjuán

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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.

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BibTeX RIS

Alvar Daza, Alexandre Wagemakers, Miguel A. F. Sanjuán. 2018-03-09. Ascertaining when a basin is Wada: the merging method. https://arxiv.org/abs/1803.03480

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