arXiv subjects

Panjing Wu

Publications and source records attributed to Panjing Wu.

2 recordsLinked to original sources

arXiv2026

On the Global Curve Attractor for polynomial gluing

Pilgrim's Finite Global Attractor Conjecture has been verified for polynomials [2], 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 [19], 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.

math.DS↗

arXiv2025

Gluing polynomials along the circle

Gluing is a cut and paste construction where the dynamics of a map in a given domain is replaced by a different one, under the condition that the two agree along the gluing curve. Here we consider two polynomials with a finite super-attracting fixed point of the same degree. We prove that any two such non-renormalizable polynomials can be glued into a rational map along the Jordan boundary of the immediate basin of the super-attracting fixed point.

math.DS↗