Bộ môn Giải tích

For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce a concept of dominated splitting or exponential separation which is weaker than exponential dichotomy. Next, a characterization of dominated splitting is obtained in terms of exponential dichotomy of rescaling dynamic equations. As a consequence, we get roughness of dominated splitting. Finally, it is shown that there is a unique minimal decomposition into exponentially separated subspaces. It turn out that the integrally separated functions and technique of upper and lower functions play an essential role in dynamics of exponentially separated systems.