Optimal estimates on rotation number of almost periodic systems

Original Paper

DOI: 10.1007/s00033-005-0020-y

Cite this article as:
Feng, H. & Zhang, M. Z. angew. Math. Phys. (2006) 57: 183. doi:10.1007/s00033-005-0020-y


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 37E45Secondary 34L3037H10


Rotation numberasymmetric systemLp normalmost periodic function

Copyright information

© Birkhäuser Verlag, Basel 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina