主講人：趙麗琴  北京師范大學(xué)教授

時(shí)間：2021年11月26日9：00

地點(diǎn)：騰訊會(huì)議 725 730 864    密碼 123456

舉辦單位：數(shù)理學(xué)院

主講人介紹：趙麗琴，北京師范大學(xué)教授，博士研究生導(dǎo)師，研究方向：向量場(chǎng)的分支理論. 在極限環(huán)的分支理論方面做了一些工作. 多次主持國(guó)家自然科學(xué)基金。

內(nèi)容介紹：In this paper, we study the number of small amplitude limit cycles in arbitrary  polynomial systems. It is found that almost all the results for the number of  small amplitude limit cycles are obtained by calculating Lyapunov constants and  determining the order of the corresponding Hopf bifurcation. It is well known  that the difficulty in calculating the Lyapunov constants increases with the  increasing of the degree of polynomial systems. So, it is necessary and valuable  for us to achieve some general results about the number of small amplitude limit  cycles in arbitrary polynomial systems with degree m, which is denoted by M(m).  In this paper, by applying the method developed by C. Christopher and N. Lloyd  in 1995, and M. Han and J. Li in 2012, we first obtain the lower bounds for  M(6)-M(14), and then prove that M(m)≥m^2 if m≥23. Finally, we obtain that M(m)  grows as least as rapidly as 18/25 1/2ln2(m+2)^2ln(m+2) for all large m (it is  proved by M. Han ＆ J. Li in J. Differential Equations, 252 (2012), 3278-3304  that the number of all limit cycles in arbitrary polynomial systems with degree  m, denoted by H(m), grows as least as rapidly as 1/2ln2(m+2)^2ln(m+2).