{
  "abstract": "We investigate the dynamics of Chebyshev's method applied to the polynomial family $p_n(z)=z(z^n-1)$ for $n>1$. The resulting map is denoted by $C_n$. It is proved that the immediate basins corresponding to the non-zero roots are unbounded and simply connected. We also show that the Julia set of $C_n$ is connected. It is proved that the immediate basin of the root at the origin exhibits a different behavior: it is unbounded for $n\\leq 16$ and bounded for $n\\geq 17$. We establish that $C_n$ is convergent whenever $n\\leq 16$ or $n$ is odd. Finally, we determine the symmetry group of $C_n$ and prove that it coincides with the symmetry group of the polynomial $p_n$, thereby confirming, for this family, a conjecture proposed by Nayak and Pal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02884",
  "author_total": 2,
  "authors": [
    {
      "name": "Tarakanta Nayak"
    },
    {
      "name": "Pooja Phogat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a446kpyqd3rcs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02884",
  "fulltext_url": null,
  "id": "a446kpyqd3rcs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02884",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7207656044",
  "pdf_url": "https://arxiv.org/pdf/2609.02884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a446kpyqd3rcs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Chebyshev's method applied to polynomials with rotational symmetry",
  "title_text": "Chebyshev's method applied to polynomials with rotational symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/a446kpyqd3rcs",
  "venue": "arXiv",
  "versions": []
}