Geodesic
On the Riemann--Hilbert problem for difference and $q$-difference systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 326-343

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We study an analog of the classical Riemann–Hilbert problem stated for the classes of difference and $q$-difference systems. We generalize Birkhoff's existence theorem. 
@article{TM_2017_297_a17,
     author = {I. V. Vyugin and R. I. Levin},
     title = {On the {Riemann--Hilbert} problem for difference and $q$-difference systems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {326--343},
     publisher = {mathdoc},
     volume = {297},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_297_a17/}
}
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I. V. Vyugin; R. I. Levin. On the Riemann--Hilbert problem for difference and $q$-difference systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Order and chaos in dynamical systems, Tome 297 (2017), pp. 326-343. http://geodesic.mathdoc.fr/item/TM_2017_297_a17/