Some ergodic properties of commuting diffeomorphisms

Abstract. For a smooth ZZ2−action on a C ∞ compact Riemannian manifold M, we discuss its ergodic properties which include the decomposition of the tangent space of M into subspaces related to Lyapunov exponents, the existence of Lyapunov charts, and the subaddtivity of entropies. In this paper we discuss some ergodic properties of commuting diffeomorphisms on a C ∞ compact Riemannian manifold concerning Lyapunov exponents and entropies. Let M be a compact C ∞ Riemannian manifold without boundary, f, g ∈ Diff2(M) with fg = gf, where fg denote the composition of f and g. In fact f and g generate a smooth ZZ2−actio