Lecture Room B, 4th Floor, The 3rd General Building, NTHU
(清華大學綜合三館 4樓B演講室)
Dynamics of almost periodic scalar parabolic equations on the circle
Yi Wang (University of Science and Technology of China)
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 dimVc(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.
