Asymptotics for solutions of periodic difference systemsSupported in part by Fondecyt 1030535, 1080034, DGI-MATH UNAP 2008 and Diufro 120521.

Supported in part by Fondecyt 1030535, 1080034, DGI-MATH UNAP 2008 and Diufro 120521.

Abstract

Using dichotomies and periodic conditions, we obtain asymptotic formulas for solutions of a difference system of Poincaré type with periodic coefficients. Some results about the theory of existence of periodic solutions for linear difference systems are presented. At the end, an open problem on the asymptotic spectral representation is proposed.

Keywords:

• Poincaré systems
• periodic solutions
• Floquet theory
• Levinson theorem
• asymptotic formulas

Acknowledgements

The authors thank the referees for the useful corrections proposed.

Notes

Supported in part by Fondecyt 1030535, 1080034, DGI-MATH UNAP 2008 and Diufro 120521.

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Additional information

Notes on contributors

Alejandro Omón Arancibia

1