From Pikovsky-Rabinovich Dynamical System to Lagrange-Hamilton Geometrical Objects

The aim of this paper is to develop, via the least squares variational method, the Lagrange-Hamilton geometries (in the sense of nonlinear connections, d-torsions and Lagrangian Yang-Mills electromagnetic-like energy) produced by Pikovsky-Rabinovich dynamical system from cryptography. From a geometrical point of view, the Jacobi stability of the Pikovsky-Rabinovich system is discussed.