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

Abstract The Kaplan–Yorke dimension can be derived using a linear interpolation between an h -dimensional Lyapunov exponent λ ( h ) > 0 and an h + 1 -dimensional Lyapunov exponent λ ( 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.

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