Entropy formula for random dynamical systems: relations between entropy, exponents and dimension

In this paper we consider random dynamical systems generated by compositions of one-sided independent and identically distributed random diffeomorphisms of class C-2 on a compact manifold. We prove an entropy formula for such random dynamical systems without assuming the SRB condition. This result is the random version of the main result obtained by Ledrappier and Young (The metric entropy of diffeomorphisms. Part II: Relations between entropy, exponents and dimension. Ann. Math. 122 (1985), 540-574).Mathematics, AppliedMathematicsSCI(E)4ARTICLE1907-19312