题目: Polynomial curve systems are exponentially decaying

主讲人: 张高飞 教授 （南京大学）

时间: 2026.06.30 14:00-16:00

地点: 中国矿业大学（北京）逸夫楼 1537

摘要: The existence of a finite global attractor for polynomial curve system has been known since the work of Belk et al. However, except in the hyperbolic case, the rate at which the pullback of a curve under a polynomial converges to the attractor remained unclear. In this work, we introduce the notions of quick returns and barrier lakes to analyze the combinatorial models of curves. These concepts allow us to show that if a certain number of successive pullbacks do not decrease the complexity of the curve by a definite proportion, then the curve admits a thick–thin decomposition: most of the curve is organized into finitely many disjoint annuli whose core curves have bounded homotopy type. In this case, we can show that some number of successive pullbacks must decrease the complexity of the curve by a definite factor. This implies that the complexity of a curve C decreases exponentially under iteration of the pullback by a polynomials. Consequently, the pullback of a curve contracts exponentially to the attractor. In particular, this provides a quantitative proof of the finite global attractor conjecture for the polynomial case.

主讲人简介: 张高飞，南京大学数学学院教授，博士生导师，国家杰出青年基金获得者。研究方向为复动力系统，在Invent.Math.,Adv.Math.等国际著名数学杂志发表学术论文多篇。欢迎广大师生参加！

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