New results for estimation 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 estimates. A close relationship with uniform asymptotic stability 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.