Almost automorphy of minimal sets for C1${C}^{1}$‐smooth strongly monotone skew‐product semiflows on Banach spaces

We focus on the presence of almost automorphy in strongly monotone skew-product semiflows Banach spaces. Under $C^1$-smoothness assumption, it is shown that any linearly stable minimal set must be automorphic. This extends celebrated result Shen and Yi [Mem. Amer. Math. Soc. 136(1998), No. 647] for classical $C^{1,\alpha}$-smooth systems. Based this, one can reduce regularity periodically forced differential equations obtain automorphic phenomena a wider range.