{
  "abstract": "In this work, we discover an intriguing Liénard system which is integrable near infinity, integrable near zero and having Ilyashenko-Kotova lips in between. Moreover, we give a necessary and sufficient condition of polynomial Liénard system with center at infinity. In a different direction we improve a lower bound on Hilbert number for Liénard systems. The improvement is due to development of Brudnyi method of calculation of cyclicity of centers near infinity and near zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.17773",
  "author_total": 4,
  "authors": [
    {
      "name": "Hebai Chen"
    },
    {
      "name": "Dehong Dai"
    },
    {
      "name": "Vadim Kaloshin"
    },
    {
      "name": "Zhijie Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fbd2zxjydb8k2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.17773",
  "fulltext_url": null,
  "id": "fbd2zxjydb8k2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.17773",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2608|Advanced Differential Equations and Dynamical Systems"
    ]
  ],
  "openalex": "W7203775011",
  "pdf_url": "https://arxiv.org/pdf/2608.17773",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fbd2zxjydb8k2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2608.17773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.17773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Cyclicity of lips and center-focus problem at infinity",
  "title_text": "Cyclicity of lips and center-focus problem at infinity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/fbd2zxjydb8k2",
  "venue": "arXiv",
  "versions": []
}