INVARIANT MANIFOLDS ASSOCIATED TO INVARIANT SUBSPACES WITHOUT INVARIANT COMPLEMENTS : A GRAPH TRANSFORM APPROACH
INVARIANT MANIFOLDS ASSOCIATED TO INVARIANT SUBSPACES WITHOUT INVARIANT COMPLEMENTS : A GRAPH TRANSFORM APPROACH
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与无不变补的不变子空间相关的不变流形:一种图变换方法
DOI：
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发表时间：
2008
期刊：
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通讯作者：
La Llave
中科院分区：
文献类型：
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作者：
R. De;La Llave
利用图变换的方法证明了在线性化的不变子空间相切的不动点附近的不动流形的存在性。与最著名的定理相反，我们不假设线性映射的对应空间是谱子空间。实际上，我们允许不存在不变补（特别是，我们不需要分解对应于谱子空间）。我们也不需要限定在空间上的算子的谱满足通常的支配条件。我们证明了一些唯一性定理，并展示了如何用它来证明流的结果。在[CFdlL03a]中用另一种方法证明了更一般的定理。
We use the graph transform method to prove existence of invariant manifolds near fixed points of maps tangent to invariant subspaces of the linearization. In contrast to the best known of such theorems, we do not assume that the corresponding space for the linear map is a spectral subspace. Indeed, we allow that there is no invariant complement (in particular, we do not need that the decomposition corresponds to spectral subspaces). We also do not need that the spectrum of the operator restricted to the spaces satisfies the usual dominance conditions. We prove some uniqueness theorems and show how this can be used to prove results for flows. More general theorems have been proved in [CFdlL03a] by another method.