Weighted limits for Poincaré difference equations. (November 2015)

• Record Type: Journal Article
• Authors: Chieocan, Rotchana; Pituk, Mihály
• Is Part Of: Applied mathematics letters. Volume 49(2015:Nov.)
• Page Start: 51
• Page End: 57
• Publication Date: 2015-11
• Subjects: Poincaré difference equation -- Growth rate -- Weighted limit -- Normalized sequence; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.04.010
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The Poincaré difference equation x n + 1 = A n x n, n ∈ N, is considered, where A n, n ∈ N, are complex square matrices such that the limit A = lim n → ∞ A n exists. It is shown that under appropriate spectral conditions certain weighted limits of the nonvanishing solutions exist. In the case when the entries of the coefficients A n, n ∈ N, and the initial vector x 0 are real our result implies the convergence of the normalized sequence x n ‖ x n ‖, n ∈ N, to a normalized eigenvector of the limiting matrix A .