Publicação
Dynamics of the coquaternionic maps x^2 + bx
| Resumo: | This paper deals with the dynamics of the one-parameter family of coquaternionic quadratic maps x2+ bx. By making use of recent results for the zeros of one-sided coquaternionic polynomials, the fixed points are analytically determined. The stability of these fixed points is also addressed, where, in some cases, due to the appearance of sets of non-isolated points, a suitably adapted notion of stability is used. The results obtained show clearly that this family is not dynamically equivalent to the simpler family x2+ c previously studied by the authors. Some numerical examples of other dynamics beyond fixed points are also presented. |
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| Autores principais: | Falcão, M. I. |
| Outros Autores: | Miranda, Fernando; Severino, Ricardo; Soares, M. J. |
| Assunto: | Coquaternionic polynomials Coquaternions Fixed points Iteration of quadratic maps Ciências Naturais::Matemáticas |
| Ano: | 2023 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | This paper deals with the dynamics of the one-parameter family of coquaternionic quadratic maps x2+ bx. By making use of recent results for the zeros of one-sided coquaternionic polynomials, the fixed points are analytically determined. The stability of these fixed points is also addressed, where, in some cases, due to the appearance of sets of non-isolated points, a suitably adapted notion of stability is used. The results obtained show clearly that this family is not dynamically equivalent to the simpler family x2+ c previously studied by the authors. Some numerical examples of other dynamics beyond fixed points are also presented. |
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