Abstract
The metric entropy of a C 2-diffeomorphism with respect to an invariant smooth measure μ is equal to the average of the sum of the positive Lyapunov exponents of μ. This is the celebrated Pesin's entropy formula, h μ ( f)=∫ M ∑ λ i >0 λ i . The C 2 regularity (or C 1+ α ) of diffeomorphism is essential to the proof of this equality. We show that at least in the two dimensional case this equality is satisfied for a C 1-generic diffeomorphism and in particular we obtain a set of volume preserving diffeomorphisms strictly larger than those which are C 1+ α where Pesin's formula holds. To cite this article: A. Tahzibi, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 1057–1062.
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