Reducibility of Quasiperiodic LinearEquations close to Constant Coe cients

Abstract

Let us consider the diierential equation _ x = (A + "Q(t; "))x; j"j " 0 ; where A is an elliptic constant matrix and Q depends on time in a quasiperi-odic (and analytic) way. It is also assumed that the eigenvalues of A and the basic frequencies of Q satisfy a diophantine condition. Then it is proved that this system can be reduced to _ y = (A (") + "R (t; "))y; j"j " 0 ; where R is exponentially small in ", and the linear change of variables that performs such reduction is also quasiperiodic with the same basic frequencies than Q. The results are illustrated and discussed in a practical example.

Cite this paper

@inproceedings{Jorba2007ReducibilityOQ, title={Reducibility of Quasiperiodic LinearEquations close to Constant Coe cients}, author={Angel Jorba and Rafael Ram rez-Ros and Jordi Villanueva}, year={2007} }