Optimal estimates on rotation number of almost periodic systems

Original Paper

Abstract.

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

Mathematics Subject Classification (2000).

Primary 37E45 Secondary 34L30 37H10 

Keywords.

Rotation number asymmetric system Lp norm almost periodic function 

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Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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