无穷维空间上的双曲不变流形的拓扑稳定性

设$A$为$Banach$空间$W$上的一个正定扇形算子,$M$为$W$上的发展方程$partial_{t}u+Au=F(u)$所生成的半群$S_{1}(t)$的紧双曲不变流形.我们将证明对任意给定的$epsilon>0$, 存在$delta>0$,对$|G|_{{A;C^1(Omega)}}

Topological Stability of Hyperbolic Invariant Manifolds in the Infinite Dimensional Space

Let A be a positive sectorial operator on a Banach space W,M be a compact hyperbolic invariant manifold for a semigroup St （t） generated by a given evolutionary equation δtu ＋Au = F （u） on the Banach space IV. We prove that for an arbitrary ε 〉0, there is a δ 〉0, such that if ｜｜ G ｜｜ { A;C1（Ω）}〈δ , then there is a continuous mapping h：M→W and a strictly increasing function φ：R＋→R＋ , one has ｜｜ Aβ（h -I） ｜｜ 〈2ε, and for the semigroup S2（t） generated by the evolu- tionary equation δty ＋Ay = F（y） ＋ G（y）, with the property that h o S1 （φ（t）） = S2 （t） o h in M.