Geodesic
The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 4-21

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The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of its sigma function. As an application, solutions of the corresponding families of polynomial dynamical systems in $C^4$ with two polynomial integrals are constructed. These systems were introduced by Buchstaber and Mikhailov on the basis of commuting vector fields on the symmetric square of algebraic curves.
Keywords: Abelian functions, hyperelliptic sigma functions, polynomial dynamical systems, commuting vector fields, symmetric products of algebraic curves. 
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     title = {The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     year = {2017},
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T. Ayano; V. M. Buchstaber. The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 4-21. http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a0/