On the Global Curve Attractor for polynomial gluing
Dynamical Systems
2026-05-04 v1
Abstract
Pilgrim's Finite Global Attractor Conjecture has been verified for polynomials [1], but remains open for general rational maps. In this paper, we prove the conjecture for a family of rational maps obtained by gluing two PCF polynomials along the boundaries of their finite superattracting basins. Adapting the idea of [17], we show that a suitably defined intersection number with a finite family of separating arcs eventually decays under pullback, yielding a finite collection of homotopy classes that attracts all non-peripheral curves under iteration.
Keywords
Cite
@article{arxiv.2605.00633,
title = {On the Global Curve Attractor for polynomial gluing},
author = {Panjing Wu},
journal= {arXiv preprint arXiv:2605.00633},
year = {2026}
}