Optimal estimates on rotation number of almost periodic systems
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.
- Publication:
-
Zeitschrift Angewandte Mathematik und Physik
- Pub Date:
- March 2006
- DOI:
- 10.1007/s00033-005-0020-y
- Bibcode:
- 2006ZaMP...57..183F
- Keywords:
-
- Primary 37E45;
- Secondary 34L30;
- 37H10;
- Rotation number;
- asymmetric system;
- L<SUP>p</SUP> norm;
- almost periodic function