Generalized Lyapunov Exponents in High-Dimensional Chaotic Dynamics and Products of Large Random Matrices

摘要

The behavior of the generalized Lyapunov exponents for chaotic symplectic dynamical systems and products of random matrices in the limit of large dimensions D are studied. For products of random matrices without any particular structure the generalized Lyapunov exponents become equal in this limit and the value of one of the generalized Lyapunov exponents is obtained by simple arguments. However, for random symplectic matrices with peculiar structures and for chaotic symplectic maps the generalized Lyapunov exponents are different also for D tends to infinity indicating that high dimensionality cannot always destroy intermittency.