Asymptotic solutions of nondiagonal linear difference systems

Authors

  • Raul Naulin
  • Manuel Pinto

DOI:

https://doi.org/10.5556/j.tkjm.31.2000.392

Abstract

This paper, relying on dichotomic properties of the matrix difference system $ W(n+1)=A(n)W(n)A^{-1}(n)$, gives conditions under which a perturbed system $ y(n+1)=(A(n)+B(n))y(n)$, by means of a nonautonomous change of variables $ y(n)=S(n)x(n)$, can be reduced to the form $ x(n+1)=A(n)x(n)$. From this, a theory of asymptotic integration of the perturbed system follows, where the linear system $ x(n+1)=A(n)x(n)$ is nondiagonal. As a consequence of these results, we prove that the diagonal system $ x(n+1)=\Lambda(n)x(n)$ has a Levinson dichotomy iff system $ W(n+1)=\Lambda(n)W(n)\Lambda^{-1}(n)$ has an ordinary dichotomy.

Author Biographies

Raul Naulin

Universidad de Oriente, Cumana 6101-A. Apartado 245. Venezuela.

Manuel Pinto

Facultad de Ciencias. Universidad de Chile, Casilla 653. Santiago. Chile.

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Published

2000-09-30

How to Cite

Naulin, R., & Pinto, M. (2000). Asymptotic solutions of nondiagonal linear difference systems. Tamkang Journal of Mathematics, 31(3), 175-192. https://doi.org/10.5556/j.tkjm.31.2000.392

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Section

Papers