| Abstract: | In this paper, we will give some optimal estimates on the rotation number of the linear equation $ifmmodeexpandafterddotelseexpandafter"fi{x} + p(t)x = 0,$ifmmodeexpandafterddotelseexpandafter"fi{x} + p(t)x = 0, and that of the asymmetric equation: $ifmmodeexpandafterddotelseexpandafter"fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,$ifmmodeexpandafterddotelseexpandafter"fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0, where p(t) and q(t) are almost periodic functions and x + = max{ x,0} , x - = min{ x,0} .x_{ + } = max { x,0} ,;x_{ - } = min { x,0} . These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions. |
