The fundamental matrix for the Jacobi equation with random coefficients

Abstract

A numerical simulation of the fundamental matrix for the Jacobi equation with random curvature is performed. The results are given for the two representations of the fundamental matrix. The first one is specified by the physical interpretation of the solution, whereas the second one is due to the characteristics of the matrix itself. The specific features of these representations are discussed. The behavior of the fundamental matrix corresponds to the main theoretical concepts based on the known theorems concerning the product of large numbers of unimodular random matrices and sometimes complements these concepts.