Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 57 min ago
PreprintCC BY 4.0arXiv

Non-uniqueness of characteristic curves of folding rational maps

  • Luxian Yang
  • Jinsong Zeng
Open at sourcePDFDOICite

Abstract

A folding rational map is a postcritically finite rational map f admitting an essential Jordan curve β, disjoint from the postcritical set Pf, whose preimage is disconnected and consists of Jordan curves homotopic to β relative to Pf. Such β is called a characteristic curve of f. We construct a real postcritically finite rational map f of degree $6$ with #Pf=4, which admits two non-homotopic characteristic curves β and β'. It is hyperbolic with orbifold signature (2,2,3,∞). This non-uniqueness is not a Lattès phenomenon, nor does it arise from a mating decomposition. The map is constructed piecewise, and a numerical model is provided to illustrate its dynamics. Thurston obstructions are excluded by arc-lifting and intersection-number arguments.

Related

  1. Uniqueness of the maximal function field with the third largest genus in characteristic $3$
    Peter Beelen, Maria Montanucci, Jonathan Niemann
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Automorphisms of ℙ1-bundles over rational surfaces in positive characteristic
    Jérémy Blanc, Ronan Terpereau
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Higher arithmetic degrees of dominant rational self-maps
    Nguyen-Bac Dang, Dragos Ghioca, Fei Hu +2
    Annali della Scuola Normale Superiore di Pisa. Classe di ScienzePeer-reviewedHAL deposit licenceFull text4 citedAlgebra & number theoryHAL
  4. Transverse rational curves and the LeBrun--Salamon conjecture
    Zhengyu Hu, Kefeng Liu, Xueyuan Wan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. A Quadratic Bound for Automorphism Groups of Curves of Positive p-Rank in Odd Characteristic
    Saeed Tafazolian
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{yang2026nonuniqueness,
  title = {{Non-uniqueness of characteristic curves of folding rational maps}},
  author = {Luxian Yang and Jinsong Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16576},
  eprint = {2609.16576},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16576},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-uniqueness of characteristic curves of folding rational maps
AU  - Luxian Yang
AU  - Jinsong Zeng
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16576
UR  - https://arxiv.org/abs/2609.16576
AB  - A folding rational map is a postcritically finite rational map f admitting an essential Jordan curve β, disjoint from the postcritical set P_f, whose preimage is disconnected and consists of Jordan curves homotopic to β relative to P_f. Such β is called a characteristic curve of f. We construct a real postcritically finite rational map f of degree $6$ with #P_f=4, which admits two non-homotopic characteristic curves β and β'. It is hyperbolic with orbifold signature (2,2,3,∞). This non-uniqueness is not a Lattès phenomenon, nor does it arise from a mating decomposition. The map is constructed piecewise, and a numerical model is provided to illustrate its dynamics. Thurston obstructions are excluded by arc-lifting and intersection-number arguments.
ER  -