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arXiv · 2610.22870

Continuity of biaccessibility dimension for polynomials

Yan Gao
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Abstract

For a polynomial $f$ of degree $d\geq 2$, 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 $f\mapsto {\rm dim}_H(B(f))$ is continuous on the entire space of degree-$d$ polynomials. Therefore $(\log d){\rm dim}_H (B(f))$ gives a continuous extension of classical core entropy from the postcritically finite case to all polynomials of degree $d$.

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Yan Gao. 2026-10-16. Continuity of biaccessibility dimension for polynomials. https://arxiv.org/abs/2610.22870

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