Chebyshev's method applied to polynomials with two distinct roots
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912785305174016 |
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| author | Nayak, Tarakanta Phogat, Pooja |
| author_facet | Nayak, Tarakanta Phogat, Pooja |
| contents | The Julia set of the Chebyshev's method applied to polynomials with exactly two distinct roots is shown to be connected, and its Fatou set is proved to be the union of attracting basins corresponding to the two roots. Further, if the two roots have the same multiplicity then the common boundary of the two immediate basins is proved to be a connected subset of the Julia set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chebyshev's method applied to polynomials with two distinct roots Nayak, Tarakanta Phogat, Pooja Dynamical Systems 37F10, 65H05 The Julia set of the Chebyshev's method applied to polynomials with exactly two distinct roots is shown to be connected, and its Fatou set is proved to be the union of attracting basins corresponding to the two roots. Further, if the two roots have the same multiplicity then the common boundary of the two immediate basins is proved to be a connected subset of the Julia set. |
| title | Chebyshev's method applied to polynomials with two distinct roots |
| topic | Dynamical Systems 37F10, 65H05 |
| url | https://arxiv.org/abs/2512.20079 |