主持人：倪明康
报告摘要：
Given a family of vector fields parametrized by ξ in its linear part, one usually obtains its versal unfolding by the so-called two-step approach. It is also a common practice to suspend ξ and calculate normal forms of the extended system. In this work we reformulate normal forms on modules of homogeneous polynomials over the ring of all continuous functions of ξ and give a direct computation of versal unfolding. Our procedure enables us to determine coefficients of all terms of a certain degree in the normal form before we give a near-identity transformation of this degree. We can give all available near-identity transformations and choose an appropriate one to eliminate more terms of higher degree for a simpler normal form. We prove that the normal form reduced in our procedure is the simplest and unique. We illustrate our method with systems of linear centre and nilpotent linear parts separately.
报告人简介：
张伟年, 四川大学二级教授，从事微分方程与动力系统研究。80年考入北京大学数学系，87年获中科院硕士，90年获北京大学博士。曾应邀到英国华威(Warwick)大学、加拿大滑铁卢(Waterloo)大学、美国杨伯翰（Brigham Young）大学、德国克劳斯塔(Clausthal)理工大学、法国南特(Nantes)中央大学、波兰西里西亚(Silesian)大学、西班牙巴塞罗那自治大学等讲学或科研合作。获得国务院“政府特殊津贴”、“中国青年科技奖”、教育部“高校青年教师奖”、宝钢优秀教师特等奖提名奖、教育部自然科学一等奖。
