Numeration and Comparison of Two Kinds of Lyapunov Dimensions in Autonomous Chaotic Flows

The relation and the difference of two kinds of Lyapunov dimensions in autonomous chaotic flows is investigated, namely, Kaplan-Yorke dimension and Sprott dimension. The former was conjectured by Kaplan and Yorke, and the latter was constructed by J.C. Sprott by using a polynomial interpolation rather than a linear one of Kaplan-Yorke dimension, but both are approximated from the spectrum of Lyapunov exponents. The attractors are selected from lower to higher dimensions, even one has a dimension almost reaching to 3 or in excess of 3. The differences of these two dimensions in autonomous chaotic attractors are made clear with nonlinear time series analysis and the results are illustrated by Lyapunov-exponent spectrum, Lyapunov dimension and so on. The approximation of these two dimensions is interpreted and compared with the correlation dimension for every chaotic attractor respectively.