时间：2026年10月29日（星期四）10:30-11:30
地点：西湖大学云谷校区E14-215
主讲人：Matteo Ruggiero, Université Paris Cité, Sorbonne Université, CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche
报告题目：Polynomial skew-products with small relative degree
报告摘要：Motivated by our recent works around the Dynamical Manin-Mumford problem for polynomial endomorphisms of C^2, we investigate the local dynamics of polynomial skew products of the form (z^d, w^c + zh(z,w)), under the condition 2 <= c < d (small relative degree).
For these maps, the asymptotic contraction rate of any point p exists and is either c or d.
We show that the locus W where the latter situation happens, analogous of the super-stable manifold in our setting, is the support of a pluripolar the Green current T introduced by Favre-Jonsson.
Moreover, under a natural condition on the dynamics of the critical branches, we describe T as an average of currents of integration along a Cantor set of holomorphic curves.
This structure can be elegantly interpreted through the induced dynamics on the Berkovich affine line over the field of Laurent series.
This is a joint work with Romain Dujardin and Charles Favre.
