Weighted limits for Poincaré difference equations

Rotchana Chieocan, Mihály Pituk

Research output: Contribution to journalArticle

Abstract

The Poincaré difference equation xn+1 = Anxn, n ∈ ℕ, is considered, where An, n ∈ ℕ, are complex square matrices such that the limit A = limn→ An 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 An, n ∈ ℕ, and the initial vector x0 are real our result implies the convergence of the normalized sequence xn/∥xn∥, n ∈ ℕ, to a normalized eigenvector of the limiting matrix A.

Original languageEnglish
Pages (from-to)51-57
Number of pages7
JournalApplied Mathematics Letters
Volume49
DOIs
Publication statusPublished - May 17 2015

Keywords

  • Growth rate
  • Normalized sequence
  • Poincaré difference equation
  • Weighted limit

ASJC Scopus subject areas

  • Applied Mathematics

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