学术活动(2021-3)

孙宪波《yclicity of periodic annulus and...

发布者:数学与统计学院   发布时间:2021-03-13  浏览次数:23

系列学术活动之(2021-3

    目:

Cyclicity of periodic annulus and Hopf cyclicity in perturbing a   hyper-elliptic Hamiltonian system with a degenerate heteroclinic loop

    要:

In this talk, we discuss  the   cyclicity of  periodic annulus and Hopf   cyclicity in perturbing a quintic Hamiltonian system.  The undamped  system is hyper-elliptic, non-symmetric   with  a degenerate heteroclinic loop,   which    connects a hyperbolic saddle   to a nilpotent saddle.  We  rigorously prove that the cyclicity is  $3$ for periodic annulus  when the weak damping term has the same   degree as that of the associated Hamiltonian system.    When the smooth  polynomial    damping term has  degree $n$,   first, a transformation    based on the   involution of the Hamiltonian is introduced, and then  we analyze the   coefficients involved  in the bifurcation function to show that   the Hopf cyclicity is    $\big[\frac{2n+1}{3}\big]$.    Further, for piecewise smooth polynomial damping with a switching   manifold at the $y$-axis, we consider the damping terms to have    degrees $l$ and $n$, respectively, and   prove that the Hopf cyclicity of the origin is $\big[\frac{3l+2n+4}{3}\big]$   ($\big[\frac{3n+2l+4}{3}\big]$) when $l\geq n$  ($n\geq l$).

人:

孙宪波,教授,广西财经学院

    间:

2021314 14:00--16:00

    点:

线上报告

报告人简介:

孙宪波,广西财经学院教授,广西杰出青年基金获得者。主要从事微分方程定性理论及其应用研究。主持2项国家自然科学基金,在DCDSJSCBSMJDE等业内期刊上发表学术论文20余篇。