Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
朱长荣 教授，重庆大学
Inviter:
周喆 博士
Title:
From homoclinic to invariant manifold
Time & Venue:
2018.11.1 14:30 N613
Abstract:
We investigate bifurcations of a degenerate homoclinic loop in $\mathbb{R}^N$. We prove that a homoclinic finger-ring, an invariant manifold of a definite dimension textured with homoclinic orbits, arises from the degenerate homoclinic orbit. The size of the homoclinic finger-ring is decided by not only its dimension of manifold but also its width. For the rise of homoclinic finger-rings of different dimensions we give conditions, which are proved to form bifurcation manifolds in the parameter space. We further estimate the width for the homoclinic finger-ring and give a method to compute the bifurcation manifolds approximately.