Lyapunov exponents for continuous transformations and dimension theory Discrete Contin

Abstract. We generalize the concept of Lyapunov exponent to trans-formations that are not necessarily differentiable. For fairly large classes of repellers and of hyperbolic sets of differentiable maps, the new expo-nents are shown to coincide with the classical ones. We also discuss the relation of the new Lyapunov exponents with the dimension theory of dynamical systems for invariant sets of continuous transformations. 1