We present a comparative study of several dynamical systems of increasing complexity, namely, the logistic map with additive noise, one, two and many globally coupled standard maps, and the Hamiltonian mean field model (i.e., the classical inertial infinitely ranged ferromagnetically coupled XY...

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann–Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs...

We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore [Phys. Rev. Lett. 64 (1990)...