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.
|Title of host publication||The 2000 IEEE International Symposium on Circuits and Systems, (ISCAS 2000) 28-31 May 2000, Geneva|
|Place of Publication||Piscataway|
|Publisher||Institute of Electrical and Electronics Engineers|
|Publication status||Published - 2000|