Speaker : Professor Jean-Yves Briend ( Universite de Provence Aix-Marseille I)
Title : On polynomial dynamical systems
Time : 2013-06-20 (Thu) 15:10 - 16:10
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: Let F: Ak+1→Ak+1 be a polynomial map with F = (F0,…, Fk) such that Q[x0,…,xk] are homogeneous polynomials of degree d2 without common zeros except the origin (0,…,0). In this talk, we’ll give a survey of several important results in the theory of dynamical systems arising from the iteration of F. In particular, we'll focus on the set of preperiodic points which is defined over an algebraic closure of the rational numbers. We'll discuss the arithmetic nature of . When F is viewed as defined over a local field such as the complex numbers C or the p-adic field , the study of the distribution of . gives important information about the dynamics of F. When k =1, we will put our attention to the study p-adic Julia set and its relationship with the so called weak Neron model.