Key points are not available for this paper at this time.
F. Ledrappier, L.-S. Young, The Metric Entropy of Diffeomorphisms: Part II: Relations between Entropy, Exponents and Dimension, Annals of Mathematics, Second Series, Vol. 122, No. 3 (Nov., 1985), pp. 540-574
Ledrappier et al. (Fri,) studied this question.