Can a polynomial interpolation improve on the Kaplan–Yorke dimension?

The Kaplan–Yorke dimension can be derived using a linear interpolation between an h  -dimensional Lyapunov exponent λ(h)>0λ(h)>0 and an h+1h+1-dimensional Lyapunov exponent λ(h+1)<0λ(h+1)<0. In this Letter, we use a polynomial interpolation to obtain generalized Lyapunov dimensions and study the relationships among them for higher-dimensional systems.