Differential equations with almost periodic coefficents

Yingfei Yi, Georgia Tech and Newton Institute

The lecture shall introduce a new point of view to the study of differential equations with almost periodic time dependence, an area which can be traced back to the 1920's and has attracted a vast amount of research in the past. It will show that the notion of almost automorphy, which was first introduced by S.~Bochner in 1955 to generalize that of almost periodicity, is fundamental and plays an essential role to the dynamics of almost periodic systems. This is due to the fact that, in a large class of almost periodic ordinary, partial and functional differential equations, almost automorphic solutions often exist but almost periodic ones may not. Other issues concerning with almost automorphic dynamics, e.g., harmonic behavior, ergodicity, stability, complexity and bifurcation, shall also be discussed.