论文标题
Nilpotent抛物线点的不变流形
Differentiable invariant manifolds of nilpotent parabolic points
论文作者
论文摘要
我们考虑了类$ c^r $的地图$ f $，其中具有抛物线类型的固定点，其差异是不可对角线的，我们使用参数化方法研究了与固定点相关的不变歧管的存在和规律性。具体而言，我们表明，在适当的条件下，$ f $的系数有$ f $的系数，$ c^r $从固定点出现了不变的曲线，并且当$ f $分析时它们是分析性的。可不同的结果是作为纤维收缩定理的应用。我们还提供了一种算法来计算不变曲线参数化的近似值，以及$ f $的限制动力学的正常形式。
We consider a map $F$ of class $C^r$ with a fixed point of parabolic type whose differential is not diagonalizable and we study the existence and regularity of the invariant manifolds associated with the fixed point using the parameterization method. Concretely, we show that under suitable conditions on the coefficients of $F$, there exist invariant curves of class $C^r$ away from the fixed point, and that they are analytic when $F$ is analytic. The differentiability result is obtained as an application of the fiber contraction theorem. We also provide an algorithm to compute an approximation of a parameterization of the invariant curves and a normal form of the restricted dynamics of $F$ on them.
