Invariance of Lyapunov characteristic exponents, Lyapunov exponents, and Lyapunov dimension for regular and non-regular linearizations

In the paper the question of invariance of Lyapunov exponents for regular and non-regular linearizations under the change of coordinates and time reparametrization is considered. The relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. Definition of Lyapunov dimension is generalized for non-regular linearization. The invariance of Lyapunov dimension and under time rescaling, which preserves direction, and under diffeomorphism of the phase space is demonstrated.