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Essential factors for surface homeomorphisms

  • Alejo García-Sassi
  • Fábio Tal
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Abstract

Let f be a homeomorphism of a closed orientable surface of genus at least one that is isotopic to a pseudo-Anosov homeomorphism, possibly relative to a finite invariant set. We construct an intrinsic monotone factor by collapsing the maximal continua whose iterates have uniformly bounded diameter in the universal cover. The quotient is homeomorphic to the original surface and the factor is isotopic to f and has several strongly chaotic dynamical features. It is infinitely continuum-wise expansive, tight, and topologically mixing, and it has a dense family of rotational horseshoes, dense periodic points, and a single topological homoclinic class. The factor can be taken as an area-preserving homeomorphism. The quotient preserves stable translation length on the fine curve graph and the applicable homological rotation sets. When f is C∞, a companion paper gives a unique measure of maximal entropy for the factor; it has full support and is Bernoulli.

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Cite

BibTeXRIS
BibTeX
@misc{garciasassi2026essential,
  title = {{Essential factors for surface homeomorphisms}},
  author = {Alejo García-Sassi and Fábio Tal},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16743},
  eprint = {2610.16743},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16743},
}
RIS
TY  - UNPB
TI  - Essential factors for surface homeomorphisms
AU  - Alejo García-Sassi
AU  - Fábio Tal
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16743
UR  - https://arxiv.org/abs/2610.16743
AB  - Let f be a homeomorphism of a closed orientable surface of genus at least one that is isotopic to a pseudo-Anosov homeomorphism, possibly relative to a finite invariant set. We construct an intrinsic monotone factor by collapsing the maximal continua whose iterates have uniformly bounded diameter in the universal cover. The quotient is homeomorphic to the original surface and the factor is isotopic to f and has several strongly chaotic dynamical features. It is infinitely continuum-wise expansive, tight, and topologically mixing, and it has a dense family of rotational horseshoes, dense periodic points, and a single topological homoclinic class. The factor can be taken as an area-preserving homeomorphism. The quotient preserves stable translation length on the fine curve graph and the applicable homological rotation sets. When f is C^∞, a companion paper gives a unique measure of maximal entropy for the factor; it has full support and is Bernoulli.
ER  -