A method for calculating the lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system

The relation between the Lyapunov exponent spectrum of a periodically excited non-autonomous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, which makes it more convenient to calculate the Lyapunov exponent spectrum of the dynamical system periodically excited. Following the definition of the Lyapunov dimensionD _L ^(A) of the autonomous system, the definition of the Lyapunov dimensionD _L of the non-autonomous dynamical system is also given, and the difference between them is the integer 1, namely,D _L ^(A) −D_L=1. For a quasi-periodically excited dynamical system, similar conclusions are formed. Project supported by the National Natural Science Foundation of China (No. 19772027), the Science Foundation of Shanghai Municipal Commission of Education (99A01) and the Science Foundation of Shanghai Municipal Commission of Science and Technology (No. 98JC14032).