報(bào)告題目：Normal forms of differential systems

報(bào)告人：Valery Romanovski（教授博導(dǎo)），University of Maribor

報(bào)告時(shí)間：2024年9月28日（周六）14:00-16:00

報(bào)告地點(diǎn)：明理樓C302

報(bào)告人簡(jiǎn)介：

Valery Romanovski 現(xiàn)任斯洛文尼亞馬里博爾(Maribor)大學(xué)教授, 應(yīng)用數(shù)學(xué)與理論物理中心研究員，上海師范大學(xué)特聘教授。 于1986年列寧格勒州立大學(xué)(現(xiàn)圣彼得堡國(guó)立大學(xué))獲得物理與數(shù)學(xué)科學(xué)專業(yè)哲學(xué)博士，2001年白俄羅斯國(guó)家科學(xué)院數(shù)學(xué)研究所獲物理與數(shù)學(xué)科學(xué)專業(yè)博士，主要研究方向?yàn)槲⒎址匠獭alery Romanovski教授2011年獲斯洛文尼亞科學(xué)研究杰出貢獻(xiàn)獎(jiǎng)， 主持并參與多項(xiàng)國(guó)際科研項(xiàng)目，如2017斯洛文尼亞-匈牙利“微分方程中代數(shù)方法的應(yīng)用”項(xiàng)目任首席研究員；2004、2006、2009、2012、2015斯洛文尼亞-美國(guó)雙邊項(xiàng)目任首席研究員；2008、20010、2011、2016斯洛文尼亞-俄羅斯雙邊項(xiàng)目任首席研究員等，并擔(dān)任“Qualitative Theory of Dynamical Systems”、“Journal of Applied Analysis and Computation”等SCI雜志的編委，多次擔(dān)任國(guó)際會(huì)議和講習(xí)班的主講人，組織過多次國(guó)際會(huì)議和講習(xí)班。

報(bào)告摘要：There are two ways to compute Poincaré-Dulac normal forms of systems of ODEs. Under the original approach used by Poincare and Dulac the normalizing transformation is explicitly computed. On each step, the normalizing procedure requires the substitution of a polynomial to a series. Under the other approach, a normal form is computed using Lie transformations. In this case, the changes of coordinates are performed as actions of certain infinitesimal generators. In both cases, on each step the homological equation is solved in the vector space of polynomial vector fields where each component of the vector field is a homogeneous polynomial. We present the third way of computing normal forms of polynomial systems of ODEs where the coefficients of all terms are parameters. It is shown that the space of the parameters is a kind of dual space and the computation of normal forms can be performed in the space of parameters treated as the space of generalized vector fields, which we call the semilattice vector fields. The approach provides a simple way to parallelize the normal form computations opening the way to compute normal forms up to higher order than under previously known two approaches.

主辦單位：理學(xué)院、人工智能研究院、非線性動(dòng)力系統(tǒng)研究所、

數(shù)理力學(xué)研究中心、科學(xué)技術(shù)發(fā)展研究院