Abstract
It is difficult to detect chaoticity of limit sets in systems with zero- or small positive Lyapunov exponents, called weakly chaotic systems. New indicators detecting weak chaoticity are proposed by use of the second derivative and the logarithmic function. It is shown that these new indicators can detect the weak chaos in such as the Froeschle map in which the Arnold diffusion and the Chirikov diffusion occurs according to perturbation parameter, the Boole transformation and the S-unimordal function in which sub-exponential behavior and a zero Lyapunov exponent appear.
