Geodesic
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/}
}
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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/