A generalization of Poincaré's theorem for recurrence systems

Abstract

A new proof and a genuine generalization to systems of first order equations is given from Poincaré classical theorem on ratio asymptotics of solutions of higher order recurrence equations. The asymptotic behavior of a fundamental system of solutions is obtained.

Keywords:

• Poincaré's system
• Recurrence equations
• Asymptotic behavior

Keywords:

• AMS Subject Classification: 39A10

Acknowledgement

Research supported in part by Fondecyt 8990013 and 1030535.