巴拿赫空间上$C^1$ -光滑强单调斜积半流极小集的几乎自同构
Almost automorphy of minimal sets for $C^1$-smooth strongly monotone skew-product semiflows on Banach spaces
摘要：
主要研究了巴拿赫空间上强单调斜积半流的几乎自同构的存在性。在$C^1$ -光滑性假设下，证明了线性稳定极小集必是几乎自守的.这推广了Shen和Yi [Mem.Amer.Math.Soc.136（1998），No.647]关于经典$C^{1,α}$ -光滑系统的著名结果.在此基础上，可以降低几乎周期受迫微分方程的正则性，得到更大范围内的几乎自守现象。
英文摘要：
We focus on the presence of almost automorphy in strongly monotone skew-product semiflows on Banach spaces. Under the $C^1$-smoothness assumption, it is shown that any linearly stable minimal set must be almost automorphic. This extends the celebrated result of Shen and Yi [Mem. Amer. Math. Soc. 136(1998), No. 647] for the classical $C^{1,α}$-smooth systems. Based on this, one can reduce the regularity of the almost periodically forced differential equations and obtain the almost automorphic phenomena in a wider range.
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