Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems

We define a sequence of uniform Lyapunov exponents in the setting of Banach spaces and prove that the Hausdorff dimension of global attractors is bounded from above by the Lyapunov dimension of the tangent map. This result generalizes the papers by Douady and Oesterlé (1980) and Ledrappier (1981) in finite dimension and Constantinet al. (1985) for Hilbert spaces.