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Continuity of biaccessibility dimension for polynomials
Abstract
For a polynomial f of degree d≥ 2, its biaccessible set B(f) consists of angles whose external rays are smooth and land at a point receiving at least two smooth external rays. We prove that the function f↦ dimH(B(f)) is continuous on the entire space of degree-d polynomials. Therefore (log d)dimH (B(f)) gives a continuous extension of classical core entropy from the postcritically finite case to all polynomials of degree d.
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BibTeX
@misc{gao2026continuity,
title = {{Continuity of biaccessibility dimension for polynomials}},
author = {Yan Gao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22870},
eprint = {2610.22870},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22870},
}
RIS
TY - UNPB
TI - Continuity of biaccessibility dimension for polynomials
AU - Yan Gao
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.22870
UR - https://arxiv.org/abs/2610.22870
AB - For a polynomial f of degree d≥ 2, its biaccessible set B(f) consists of angles whose external rays are smooth and land at a point receiving at least two smooth external rays. We prove that the function f↦ dim_H(B(f)) is continuous on the entire space of degree-d polynomials. Therefore (log d)dim_H (B(f)) gives a continuous extension of classical core entropy from the postcritically finite case to all polynomials of degree d.
ER -