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PreprintCC BY 4.0arXiv

Marker endomorphisms for complex Hénon maps

  • Ivan Cuezva
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Abstract

This paper investigates some properties of the compound marker endomorphisms appearing in the study of the monodromy action of Hénon maps. The main result is to present a computable criterion for checking the bijectivity of a single marker endomorphism. Some direct corollaries are also developed, keeping in mind the Hénon dynamical aspect. Another point of the paper is the reformulation of compound marker endomorphisms in terms of permutive functions, which have been introduced by Hedlund. This reformulation allows to directly apply some of his results.

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Cite

BibTeXRIS
BibTeX
@misc{cuezva2026marker,
  title = {{Marker endomorphisms for complex Hénon maps}},
  author = {Ivan Cuezva},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24449},
  eprint = {2609.24449},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24449},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Marker endomorphisms for complex Hénon maps
AU  - Ivan Cuezva
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24449
UR  - https://arxiv.org/abs/2609.24449
AB  - This paper investigates some properties of the compound marker endomorphisms appearing in the study of the monodromy action of Hénon maps. The main result is to present a computable criterion for checking the bijectivity of a single marker endomorphism. Some direct corollaries are also developed, keeping in mind the Hénon dynamical aspect. Another point of the paper is the reformulation of compound marker endomorphisms in terms of permutive functions, which have been introduced by Hedlund. This reformulation allows to directly apply some of his results.
ER  -