Basins of attraction for a quadratic coquaternionic map

M. Irene Falcão, Fernando Miranda, Ricardo Severino and M. Joana Soares

Chaos, Solitons & Fractals, 2017, vol. 104, issue C, 716-724

Abstract: In this paper we consider the extension, to the algebra of coquaternions, of a complex quadratic map with a real super-attractive 8-cycle. We establish that, in addition to the real cycle, this new map has sets of non-isolated periodic points of period 8, forming four attractive 8-cycles. Here, the cycles are to be interpreted as cycles of sets and an appropriate notion of attractivity is used. Some characteristics of the basins of attraction of the five attracting 8-cycles are discussed and plots revealing the intertwined nature of these basins are shown.

Keywords: Iteration of maps; Coquaternions; Attracting cycles; Basins of attraction (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:104:y:2017:i:c:p:716-724

DOI: 10.1016/j.chaos.2017.09.016

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