Effective reducibility of a class of linear differential equations with quasiperiodic coefficients
type: Item
instance of: scholarly article
title: Effective reducibility of a class of linear differential equations with quasiperiodic coefficients
zbMATH Open document ID: 1069.34058
author: Ren Zi Yang
author: Junxiang Xu
publication date: 2004-10-01T00:00:00Z
review text: The authors consider the effective reducibility of the linear differential equation \[ \dot x= (A+ Q(t, \varepsilon))x,\quad |\varepsilon|\leq\varepsilon_0, \] where \(A\) is a constant matrix, \(Q(t,\varepsilon)\) is quasiperiodic in \(t\), and \(\varepsilon\) is a small perturbation parameter. In fact, they consider the more general case, which embraces both the multiple eigenvalues case and the degenerate case, and prove a similar result to that due to \textit{À. Jorba}, \textit{R. Ramírez-Ros} and \textit{J. Villanueva} [SIAM J. Math. Anal. 28, No. 1, 178--188 (1997; Zbl 0866.34032)].
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 2104911
zbMATH Keywords: linear differential equations
zbMATH Keywords: effective reducibility
zbMATH Keywords: quasiperiodic
reviewed by: S. D. Bajpai
MaRDI profile type: Publication
full work available at URL: s10114-004-0339-x
OpenAlex ID: W2030680448
cites work: On the reducibility of linear differential equations with quasiperiodic coefficients
cites work: Effective Reducibility of Quasi-periodic Linear Equations Close To Constant Coefficients
cites work: On the reducibility of linear differential equations with quasiperiodic coefficients which are degenerate
cites work: PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
DOI: 10.1007/S10114-004-0339-X
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2104911