PreprintCC BY 4.0arXiv
Polynomial automorphisms of C^2 with the same equilibrium measure
Abstract
We review the following question: when do two polynomial automorphisms of C^2 have the same maximal entropy measure? While the answer has been known for some time when both automorphisms are compositions of Hénon maps, the general case is more delicate. In this (mostly expository) note we explain how recent results in random dynamics give an almost complete solution to the question, and point out a number of related open problems.
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BibTeX
@misc{dujardin2026polynomial,
title = {{Polynomial automorphisms of C^2 with the same equilibrium measure}},
author = {Romain Dujardin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37600},
eprint = {2610.37600},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37600},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Polynomial automorphisms of C^2 with the same equilibrium measure
AU - Romain Dujardin
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37600
UR - https://arxiv.org/abs/2610.37600
AB - We review the following question: when do two polynomial automorphisms of C^2 have the same maximal entropy measure? While the answer has been known for some time when both automorphisms are compositions of Hénon maps, the general case is more delicate. In this (mostly expository) note we explain how recent results in random dynamics give an almost complete solution to the question, and point out a number of related open problems.
ER -