Arithmetic aspects of discrete periodic Toda flows
Abstract
Abstract We construct a new algebraic linearization of the discrete periodic Toda flow by using Mumford’s algebraic description of the Jacobian of a hyperelliptic curve. In particular, the discrete periodic Toda flow can be expressed in terms of the famous Gauß composition law for quadratic forms adapted to the framework of hyperelliptic curves by Cantor. One remarkable consequence of our approach is a new integrality property for the discrete periodic Toda flow. This leads, in particular, to a p -adic description of the closely related periodic box-ball flow, which has very surprising connections to number theory.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Publisher
- IOP Publishing
- Volume
- 59
- Issue
- 6
- Pages
- 065205–065205
- Publication date
- 5 February 2026
- Language
- EN