### 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.

Original language | English |
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Pages (from-to) | 51-57 |

Number of pages | 7 |

Journal | Applied Mathematics Letters |

Volume | 49 |

DOIs | |

Publication status | Published - May 17 2015 |

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

Chieocan, R., & Pituk, M. (2015). Weighted limits for Poincaré difference equations.

*Applied Mathematics Letters*,*49*, 51-57. https://doi.org/10.1016/j.aml.2015.04.010