On the reducibility of a class of finitely differentiable quasi-periodic linear systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Li, Jia¹  Zhu, Chunpeng¹ 

[1] Xuzhou Inst Technol, Sch Math Phys, Xuzhou 221111, Peoples R China

关键词: Reducibility;    Finitely differentiable;    Quasi-periodic;    KAM theory;   

DOI  :  10.1016/j.jmaa.2013.10.077

来源: Elsevier

【 摘 要 】

In this paper, we consider the following system X = (A + epsilon(Q) over tilde (t))x, where A is a constant matrix with different eigenvalues, and (Q) over tilde (t) is quasi-periodic with frequencies omega(1), omega(2),...,omega(r),. Moreover, Q(theta) = Q(omega t) = (Q) over tilde (t) has continuous partial derivatives [Graphics] for j = 1,2,..., r, where b > [graphics] r + 1 is an element of Z. and the moduli of continuity of [Graphics] satisfy a condition of finiteness (condition on an integral), which is more general than a Holder condition. Under suitable hypothesis of non-resonance conditions and nondegeneracy conditions, we prove that for most sufficiently small epsilon, the system can be reducible to a constant coefficient differentiable equation by means of a quasi-periodic homeomorphism. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free