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PreprintCC BY 4.0arXiv

Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities

  • Rodrigo Arruda
  • Bernardo Carvalho
  • Piotr Oprocha
  • Alberto Sarmiento
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Abstract

We establish a complete structural classification for cwF-hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cwF-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus 𝕋2 or to a standard hyperelliptic quotient on 𝕊2 of a hyperbolic affine toral map. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.

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Cite

BibTeXRIS
BibTeX
@misc{arruda2026continuumwise,
  title = {{Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities}},
  author = {Rodrigo Arruda and Bernardo Carvalho and Piotr Oprocha and Alberto Sarmiento},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.11943},
  eprint = {2606.11943},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.11943},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities
AU  - Rodrigo Arruda
AU  - Bernardo Carvalho
AU  - Piotr Oprocha
AU  - Alberto Sarmiento
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2606.11943
UR  - https://arxiv.org/abs/2606.11943
AB  - We establish a complete structural classification for cw_F-hyperbolic surface homeomorphisms. Specifically, we prove that a surface homeomorphism is cw_F-hyperbolic if, and only if, it is a pseudo-Anosov homeomorphism whose singularities consist exclusively of spines (1-prongs). Furthermore, we classify these systems up to topological conjugacy, showing that every such homeomorphism is conjugate to either an Anosov automorphism on the torus 𝕋^2 or to a standard hyperelliptic quotient on 𝕊^2 of a hyperbolic affine toral map. As a rigid consequence of this classification, we show that such dynamics are strictly obstructed on surfaces of genus greater than one, the Klein bottle, and the projective plane.
ER  -