Multiperiodic Flows, Chaos and Lyapunov Exponents

The existence of positive Lyapunov exponents for almost all initial conditions ensures non-periodic behavior of chaotic flows. In multiperiodic flows responses to external perturbations as well as the stability of an attractor can be expressed in terms of Lyapunov exponents. In the present paper we summarize basic properties of Lyapunov exponents, and influences of external perturbations (deterministic ones, noise and diffusion) on multiperiodic flows are investigated with the aid of Lyapunov exponents. We find a new feature of onset of diffusion-induced turbulence, and a statistical-physical theory is developed in order to clarify its statistical characteristics. Furthermore a theoretical possibility of a new type of diffusion-induced turbulence will be conjectured.