论文标题
具有符号特征值附近的有限解决方案的永久性和分叉的
Permanency and bifurcations of bounded solutions near homocilincs with symetric eigenvalues
论文作者
论文摘要
我们考虑一个具有同质轨道的系统，我们分解了解决方案空间上的相应变分方程，并为在$ c^1 $ vector Fields空间中的同型层次永久性提供了足够的条件。我们还为附近有限解决方案的持久性和多个分叉提供了新的条件。我们的结果可以通过数值验证，并且不符合经典方法的局限性（例如Melnikon积分和Poincare Map）
we consider a system with homoclinic orbit, We decompose the corresponding variational equation on the space of solutions and provide sufficient conditions for the permanency of homoclinic in the space of $C^1$ vector fields. We also provide new sufficient conditions for the persistence and multiple bifurcations of the bounded solutions nearby. our results can be verified numerically and do not meet the limitations of classic methods (like Melnikon integrals and Poincare map)
