國立清華大學 數學系

Abstract: In this talk, we focus on the skew-product semiflow generated by a almost periodic spatially-homogeneous scalar reaction-diffusion equation on the circle. The structure of the minimal set M is thoroughly investigated under the assumption that its associated center space is no more than 2-dimensional. Such situation naturally occurs while, for instance, M is hyperbolic or uniquely ergodic. We show that M is a 1-cover provided that M is hyperbolic. If dimV^c(M)=1, then either M is an almost 1-cover; or can be embedded into an almost periodically forced circle-flow. This new phenomena we discovered here reinforces the possible appearance of the almost periodically forced circle flow in infinite-dimensional dynamical systems generated by certain evolutionary equations. This is a joint work with Wenxian Shen and Dun Zhou.