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PreprintCC BY-NC-SA 4.0arXiv

Non-archimedean and hybrid dynamics of regular polynomial automorphisms

  • Reimi Irokawa
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Abstract

In this paper, we study the weak limit of the invariant measures attached to an analytic family {ft}t∈𝔻* of regular polynomial automorphisms over ℂN parametrized by the unit punctured disk which may degenerate at the origin, by using the techniques called hybrid spaces developed by Boucksom--Favre--Jonsson. For each t, the invariant measure μt is constructed by Sibony, and we show that the weak limit of {μt}t over the hybrid space is given by the invariant measure of the regular polynomial automorphism fℂ((t))an over ℂ((t)) induced from the original family. This is a generalization of the author's previous result for degenerating families of dynamics of Hénon mappings.

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Cite

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BibTeX
@misc{irokawa2026nonarchimedean,
  title = {{Non-archimedean and hybrid dynamics of regular polynomial automorphisms}},
  author = {Reimi Irokawa},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06821},
  eprint = {2610.06821},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06821},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Non-archimedean and hybrid dynamics of regular polynomial automorphisms
AU  - Reimi Irokawa
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06821
UR  - https://arxiv.org/abs/2610.06821
AB  - In this paper, we study the weak limit of the invariant measures attached to an analytic family {f_t}_t∈𝔻^* of regular polynomial automorphisms over ℂ^N parametrized by the unit punctured disk which may degenerate at the origin, by using the techniques called hybrid spaces developed by Boucksom--Favre--Jonsson. For each t, the invariant measure μ_t is constructed by Sibony, and we show that the weak limit of {μ_t}_t over the hybrid space is given by the invariant measure of the regular polynomial automorphism f_ℂ((t))^an over ℂ((t)) induced from the original family. This is a generalization of the author's previous result for degenerating families of dynamics of Hénon mappings.
ER  -