The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 51-59
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By the direct Lyapunov method we prove a sufficient condition for the exponential dichotomy with weakened (in comparison with a case of arbitrary coefficients) requirements to the difference derivative of the Lyapunov function along the system trajectory. We give an illustrating example.
Keywords:
exponential dichotomy, indefinite Hermitian form, shell of an almost periodical matrix.
@article{IVM_2010_10_a4,
author = {R. K. Romanovskii and L. V. Belgart},
title = {The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients},
journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
pages = {51--59},
publisher = {mathdoc},
number = {10},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/IVM_2010_10_a4/}
}
TY - JOUR AU - R. K. Romanovskii AU - L. V. Belgart TI - The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients JO - Izvestiâ vysših učebnyh zavedenij. Matematika PY - 2010 SP - 51 EP - 59 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/IVM_2010_10_a4/ LA - ru ID - IVM_2010_10_a4 ER -
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R. K. Romanovskii; L. V. Belgart. The exponential dichotomy of solutions to systems of linear difference equations with almost periodic coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2010), pp. 51-59. http://geodesic.mathdoc.fr/item/IVM_2010_10_a4/