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Bäcklund Transformations and New Integrable Systems on the Plane

  • A. V. Tsiganov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 273)

Abstract

The hyperelliptic curve cryptography is based on the arithmetic in the Jacobian of a curve. In classical mechanics well-known cryptographic algorithms and protocols can be very useful for construct auto-Bäcklund transformations, discretization of continuous flows and study of integrable systems with higher order integrals of motion. We consider application of a standard arithmetic of divisors on genus two hyperelliptic curve for the construction of new auto-Bäcklund transformations for the Hénon-Heiles system. Another type of auto-Bäcklund transformations associated with equivalence relations between unreduced divisors and the construction of the new integrable systems in the framework of the Jacobi method are also discussed.

Keywords

Bäcklund transformations Integrable systems Hyperelliptic curve cryptography 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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