一类高维映射不变圈的计算

COMPUTING BIFURCATING INVARIANT CIRCLES FOR A HIGH DIMENSIONAL MAPPING

在一类高维映射中实现了由Iooss等人提出的映射不变圈的算法.首先分析了不变圈的分岔条件,然后通过Fredholm择一方法分析了在计算不变圈过程中出现的一类方程解的存在性,再根据不变圈上映射到自身的不变性,通过分析振幅各阶项的系数,最终在一高维映射中实现了不变圈的计算.

Based on the computation method of bifurcating invariant circles for mapping by Iooss et al, first, the condition of bifurcations of invariant circles was analyzed, then a necessary condition was put forward for the solution existence of a kind of equations, which appeared in computing invariant circles by Fredholm method, finally the computation method of bifurcating invariant circles for mapping was achieved in a three-dimensional map.