Two types of estimates of Hausdorff dimension

In this paper we present two approaches to estimate the Hausdorff dimension of an invariant compact set of a dynamical system: the method of characteristic exponents (estimates of the Kaplan-Yorke type) and the method of Lyapunov functions. In the first approach, using Lyapunov´s first method we exploit characteristic exponents for obtaining such estimate. A close relationship with uniform asymptotic stability hereby is established. A second bound for the Hausdorff dimension is obtained by exploiting Lyapunov´s direct method and thus relies on the use of certain Lyapunov functions