Geodesic
Difference Krichever--Novikov Operators of Rank~2
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 211-224

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The work is devoted to the study of one-point commuting difference operators of rank $2$. In the case of hyperelliptic spectral curves, we obtain equations equivalent to the Krichever–Novikov equations for the discrete dynamics of the Tyurin parameters. Using these equations, we construct examples of operators corresponding to hyperelliptic spectral curves of arbitrary genus.
Keywords: commuting difference operators. 
@article{TM_2019_305_a10,
     author = {G. S. Mauleshova and A. E. Mironov},
     title = {Difference {Krichever--Novikov} {Operators} of {Rank~2}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {211--224},
     publisher = {mathdoc},
     volume = {305},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_305_a10/}
}
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G. S. Mauleshova; A. E. Mironov. Difference Krichever--Novikov Operators of Rank~2. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebraic topology, combinatorics, and mathematical physics, Tome 305 (2019), pp. 211-224. http://geodesic.mathdoc.fr/item/TM_2019_305_a10/