中科院数学与系统科学研究院

数学研究所

学术报告会

报告人：Matteo Ruggiero（University Paris Diderot (Paris VII), French）

题  目：Local dynamics of non-invertible selfmaps on complex surfaces

时  间：2017.10.26（星期四），14 :30-15:30

地  点：数学院南楼N902室

摘  要：We consider the local dynamical system induced by a non-invertible selfmap f of C^2 fixing the origin.Given a modification (composition of blow-ups) over the origin, the lift of f on the modified space X defines a meromorphic map F.We say that F is algebraically stable if, for every compact curve E in X, its image F^n(E) through the iterates of F does not belong to the indeterminacy set of F for all n big enough.We show that, starting from any modification, we can blow-up some more and obtain another modification for which the lift F is algebraically stable.The proof relies on the study of the action f_* induced by f on a suitable space of valuations V.In particular we construct a distance on V for which f_* is non-expanding. This allows us to deduce fixed point theorems for f_*.If time allows, I will comment on the recent developments about local dynamics on normal surface singularities.Joint work with William Gignac.