Sacker-Sell problem in quasiperiodic case

摘要

The Sacker-Sell problem in quasiperiodic case, whether quasiperiodic linear differential systems can be quasiperiodically triangularized, is studied. A dass of more concrete quasiperiodic linear differential systems which are not quasiperiodically triangularized are given under the stronger conditions: (ⅰ) the coefficient matrix is of C~∞; (ⅱ) the frequency satisfies the Diophantine condition. A sufficient condition for quasiperiodic triangularization of quasiperiodic linear differential systems is also established.