Abstract：In this talk, we introduce the concepts of rescaled expansiveness and the rescaled shadowing property for flflows on metric spaces which are dynamical properties, and present a spectral decomposition theorem for flflows. More precisely, we prove that if a flflow is rescaling expansive and has the rescaled shadowing property on a locally compact metric space, then it admits the spectral decomposition. Moreover, we show that if a flflow on locally compact metric space has the rescaled shadowing property then its restriction on nonwandering set also has the rescaled shadowing property.
