Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps
Resonant zones, inner and outer splittings in generic and low order resonances of area preserving maps
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面积保留图的通用和低阶共振中的共振区、内部和外部分裂
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Vieiro
中科院分区：
文献类型：
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作者：
C. Simó;A. Vieiro
本文考虑一类椭圆不动点邻域内的单参数保面积映射族。随着参数的变化，产生了不同周期的双曲和椭圆周期轨道。阶数小于5的异常共振必须单独考虑。双曲周期点的不变流形是包含椭圆周期点的有界岛。一般来说，这些流形分裂。结果表明，在适当的条件下，内劈裂和外劈裂是不同的。我们提供准确的公式描述这些流形的分裂作为一个函数的参数和这些幅度的相对值作为一个函数的几何性质。数值协议说明主要使用Hénon地图作为一个例子。
We consider a one-parameter family of area preserving maps in a neighbourhood of an elliptic fixed point. As the parameter evolves hyperbolic and elliptic periodic orbits of different periods are created. The exceptional resonances of order less than 5 have to be considered separately. The invariant manifolds of the hyperbolic periodic points bound islands containing the elliptic periodic points. Generically, these manifolds split. It turns out that the inner and outer splittings are different under suitable conditions. We provide accurate formulae describing the splittings of these manifolds as a function of the parameter and the relative values of these magnitudes as a function of geometric properties. The numerical agreement is illustrated using mainly the Hénon map as an example.