PreprintarXiv licencearXiv
On the group of automorphisms of the escaping sets of Hénon maps
Abstract
In this article, we provide an explicit description of Aut1(IH+), the group of automorphisms of the escaping set IH+ of a Hénon map that induce the identity on its fundamental group. More precisely, for a Hénon map H(x,y)=(y,p(y)−δx), where p is a polynomial of degree d≥ 2 and δ≠ 0, we show that Aut1(IH+) is completely determined by the degree and the coefficients of p. Thus, the automorphism group of the escaping set, subject to the prescribed topological constraint, can be explicitly characterized in terms of the underlying Hénon map.
Related
BibTeX
@misc{mahima2026group,
title = {{On the group of automorphisms of the escaping sets of Hénon maps}},
author = {Mahima and Ratna Pal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25891},
eprint = {2610.25891},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25891},
}
RIS
TY - UNPB
TI - On the group of automorphisms of the escaping sets of Hénon maps
AU - Mahima
AU - Ratna Pal
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25891
UR - https://arxiv.org/abs/2610.25891
AB - In this article, we provide an explicit description of Aut_1(I_H^+), the group of automorphisms of the escaping set I_H^+ of a Hénon map that induce the identity on its fundamental group. More precisely, for a Hénon map H(x,y)=(y,p(y)−δx), where p is a polynomial of degree d≥ 2 and δ≠ 0, we show that Aut_1(I_H^+) is completely determined by the degree and the coefficients of p. Thus, the automorphism group of the escaping set, subject to the prescribed topological constraint, can be explicitly characterized in terms of the underlying Hénon map.
ER -